prof. dr. Franc Forstnerič

First announcement STA STA Interview DELO DELO interview
Portraits of Science (by Arne Hodalič and Katja Bidovec, National Geographic Slovenija, January 2023) Krakovski nasip

Plenary speaker, 8th European Congress of Mathematics, Portorož, 20-25 June 2021. Slides

Stefan Bergman Prize 2019 Obzornik mat. fiz. 68(2):74-81, 2021

Complex Analysis, Geometry, and Dynamics III - Portorož 2024, 10-14 June 2024

Complex Analysis, Geometry, and Dynamics II - Portorož 2023, 5-9 June 2023

Complex Analysis, Geometry and Dynamics - Portorož 2022, 20-24 June 2022

Stein Manifolds and Holomorphic Mappings 2018, Ljubljana, 17-21 September 2018 Photos

Books

Minimal Surfaces from a Complex Analytic Viewpoint (with A. Alarcón and F. J. López). Springer Monographs in Mathematics, Springer, Cham, 2021. ISBN 978-3-030-69055-7/hbk; 978-3-030-69056-4/ebook. Zbl 07332812
New complex analytic methods in the study of non-orientable minimal surfaces in Rⁿ (with A. Alarcón and F. J. López). Memoirs Amer. Math. Soc. 264:1283 (2020). Zbl 07213239 arXiv
Stein manifolds and holomorphic mappings. The homotopy principle in complex analysis. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics 56. Second Edition. Cham: Springer Internat. (ISBN 978-3-319-61057-3/hbk; 978-3-319-61058-0/ebook). xiv+562 p. (2017). Zbl 06737283
Errata for Stein manifolds and holomorphic mappings. The homotopy principle in complex analysis. January 23, 2023.
Stein Manifolds and Holomorphic Mappings. The homotopy principle in complex analysis. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge 56. Berlin: Springer (ISBN 978-3-642-22249-8/hbk; 978-3-642-22250-4/ebook). xii, 489 p. (2011). MR2975791 Zbl 1247.32001

Preprints

Runge and Mergelyan theorems on families of open Riemann surfaces. Preprint, January 2025. arXiv
Isotopies of complete minimal surfaces of finite total curvature (with Antonio Alarcón and Finnur Lárusson). Preprint, June 2024. arXiv
Oka-1 manifolds (with Antonio Alarcón). Preprint, March 2023. arXiv
Minimal surfaces for undergraduates. An introduction for students of Mathematics in connection to a first course on differential equations and the calculus of variations. No prior knowledge of differential geometry is assumed. arXiv.
Analiza na mnogoterostih. A textbook (in Slovenian) for the course "Analysis on Manifolds" within the Master program in Mathematics.

Online first publications

Oka tubes in holomorphic line bundles (with Yuta Kusakabe). Math. Ann., 28 November 2024, 2024. PDF arXiv

Research and expository papers, 2015-2024

Oka-1 manifolds: new examples and properties (with Finnur Lárusson). Math. Z., 309:2, article 26, 2025. PDF arXiv
Minimal surfaces with symmetries. Proc. London Math. Soc., 128:3, e12590, 2024. PDF arXiv
Embedded complex curves in the affine plane (with Antonio Alarcón). Ann. Mat. Pura Appl. (4), 203:1673-1701, 2024. PDF arXiv
Proper holomorphic embeddings with small limit sets. Proc. Am. Math. Soc., Ser. B, 11:77-83, 2024. PDF arXiv
Schwarz-Pick lemma for harmonic maps which are conformal at a point (with David Kalaj). Anal. PDE, 17(3):981-1003, 2024. PDF arXiv
Oka domains in Euclidean spaces (with Erlend F. Wold). Internat. Math. Res. Not., 2024(3):1801-1824, 2024. PDF arXiv
Complete nonsingular holomorphic foliations on Stein manifolds (with Antonio Alarcón). Mediterranean J. Math., 21, Article 25, 2024. PDF arXiv
Hyperbolic domains in real Euclidean spaces (with Barbara Drinovec Drnovšek). Pure Appl. Math. Q., 19(6):2689-2735, 2023. arXiv
The Calabi-Yau problem for minimal surfaces with Cantor ends. Revista Mat. Iberoam., 39(6):2067-2077, 2023. PDF arXiv
Domains without parabolic minimal surfaces and weakly hyperbolic domains. Bull. London Math. Soc., 55(6):2778-2792, 2023. PDF arXiv
Minimal surfaces in Euclidean spaces by way of complex analysis. European Congress of Mathematics, 9-43. EMS Press, Berlin, [2023], ©2023 arXiv
Embedding bordered Riemann surfaces in strongly pseudoconvex domains. Rev. Roumaine Math. Pures Appl. 68(1-2):83-94, 2023. Issue dedicated to Mihnea Colțoiu. PDF arXiv
Proper holomorphic maps in Euclidean spaces avoiding unbounded convex sets (with Barbara Drinovec Drnovšek). J. Geom. Anal., 33:170, 2023. PDF arXiv
Proper superminimal surfaces of given conformal types in the hyperbolic four-space. Ann. Fac. Sci. Toulouse Math., 32:145-172, 2023. arXiv.
Recent developments on Oka manifolds. Indag. Math., 34(2):367-417, 2023. arXiv.
Flexible domains for minimal surfaces in Euclidean spaces (with Barbara Drinovec Drnovšek). J. Math. Anal. Appl., 517(2):126653, 2023. PDF arXiv
Stein neighbourhoods of bordered complex curves attached to holomorphically convex sets. Arkiv Mat., 60(2):335-349, 2022. arXiv
Mergelyan approximation theorem for holomorphic Legendrian curves. Anal. PDE 15(4):983-1010, 2022. PDF arXiv.
The first thirty years of Andersén-Lempert theory (with Frank Kutzschebauch). Anal. Math., 48(2):489-544, 2022. arXiv
Holomorphic Legendrian curves in projectivised cotangent bundles (with F. Lárusson). Indiana Univ. Math. J., 71(1):93-124, 2022. arXiv.
Every smoothly bounded p-convex domain in Rⁿ admits a p-plurisubharmonic defining function. Bull. Sci. Math., 175:103100, 2022. arXiv
Euclidean domains in complex manifolds. J. Math. Anal. Appl., 506(1):125660, 2022. Zbl 7413100. arXiv
Holomorphic Legendrian curves in CP³ and superminimal surfaces in S⁴ (with A. Alarcón and F. Lárusson). Geom. Topol., 25(7):3507-3553, 2021. arXiv.
The Calabi-Yau problem for Riemann surfaces with finite genus and countably many ends (with A. Alarcón). Rev. Mat. Iberoam., 37(4):1399-1412, 2021. Zbl 1469.53014. arXiv.
Immersions of open Riemann surfaces into the Riemann sphere. Izv. RAN. Ser. Mat., 85(3):239-260, 2021 (Russian). English transl., Izvestiya Math., 85(3):562-581, 2021. Zbl 1470.32037. arXiv.
The Calabi-Yau property of superminimal surfaces in self-dual Einstein four-manifolds. J. Geom. Anal., 31:4754-4780, 2021. Zbl 07343425 arXiv.
Holomorphic families of Fatou-Bieberbach domains and applications to Oka manifolds (with E. Fornæss Wold). Math. Res. Lett., 27(6):1697-1706, 2020. Zbl 07317610 arXiv
H-principle for complex contact structures on Stein manifolds. J. Symplectic Geom., 18(3):733-767, 2020. Zbl 07285739 arXiv
A foliation of the ball by complete holomorphic discs (with A. Alarcón). Math. Z., 296:169-174, 2020. Full text view only. Zbl 07242438 arXiv
Holomorphic approximation: the legacy of Weierstrass, Runge, Oka-Weil, and Mergelyan (with J. E. Fornæss and E. Fornæss Wold). In: D. Breaz, M. Th. Rassias (Eds.), Advancements in Complex Analysis, pp. 133-192. Springer, Cham, 2020. Zbl 07216541 arXiv
Runge tubes in Stein manifolds with the density property (with E. F. Wold). Proc. Amer. Math. Soc., 148(2):569-575, 2020. Zbl 1436.32041 arXiv
Proper holomorphic immersions into Stein manifolds with the density property. J. Anal. Math., 139(2):585-596, 2019. Zbl 1436.32060 arXiv
Every meromorphic function is the Gauss map of a conformal minimal surface (with A. Alarcón and F.J. López). J. Geom. Anal., 29(4):3011-3038, 2019. Zbl 1432.30030 arXiv
Mergelyan's and Arakelian's theorems for manifold-valued maps. Moscow Math. J., 19(3):465-484, 2019. Zbl 07206617 arXiv
New complex analytic methods in the theory of minimal surfaces: a survey (with A. Alarcón). J. Aust. Math. Soc., 106(3):287-341, 2019. Zbl 1414.53007 arXiv
The parametric h-principle for minimal surfaces in Rⁿ and null curves in Cⁿ (with F. Lárusson). Comm. Anal. Geom., 27(1):1-45, 2019. Zbl 1414.53009 arXiv
A properly embedded holomorphic disc in the ball with finite area and dense boundary curve. Math. Ann., 373(1-2):719-742, 2019. Zbl 1426.32009 arXiv
Darboux charts around holomorphic Legendrian curves and applications (with A. Alarcón). Internat. Math. Res. Not. (IMRN), 3:893-922, 2019. Zbl 1429.53088 arXiv
Minimal surfaces in minimally convex domains (with A. Alarcón, B. Drinovec Drnovšek, and F. J. López). Trans. Amer. Math. Soc. 371(3):1735-1770, 2019. Zbl 1406.53004 arXiv
Holomorphic embeddings and immersions of Stein manifolds: a survey. In: Geometric Complex Analysis, 145-169, Springer Proc. Math. Stat., Springer, Singapore, 2018. Zbl 1404.32019 arXiv
Every conformal minimal surface in R³ is isotopic to the real part of a holomorphic null curve (with A. Alarcón). J. reine angew. Math. (Crelle's J.), 740:77-109, 2018. Zbl 1400.53011 arXiv
Divisors defined by noncritical functions. Proc. Amer. Math. Soc., 1467(7):2985-2994, 2018. Zbl 1405.32011 arXiv
The Oka principle for holomorphic Legendrian curves in C²ⁿ⁺¹ (with F. Lárusson). Math. Z., 288(1-2):643-663, 2018. Zbl 1394.53082 arXiv
Complete densely embedded complex lines in C² (with A. Alarcón). Proc. Amer. Math. Soc., 146(3):1059-1067, 2018. Zbl 1386.32016 arXiv
Surjective holomorphic maps onto Oka manifolds. In: Complex and Symplectic Geometry, 73-84, Springer INdAM Ser., 21, Springer, Cham, 2017. Zbl 1391.32019 arXiv
Hyperbolic complex contact structures on C²ⁿ⁺¹. J. Geom. Anal. 27(4):3166-3175, 2017. Zbl 1390.53087 arXiv
Holomorphic Legendrian curves (with A. Alarcón and F. J. López). Compositio Math., 153(9):1945-1986, 2017. MR 3705282 Zbl 1373.53106 arXiv
A long C² without holomorphic functions (with L. Boc Thaler). Analysis & PDE 9(8):2031-2050, 2016. MR 3599525 Zbl 1368.32008 arXiv
Proper holomorphic embeddings into Stein manifolds with the density property (with R. Andrist, T. Ritter, and E. F. Wold). J. Anal. Math., 130(1):135-150, 2016. Full text view only. MR 3574650 Zbl 1373.32015 arXiv
Noncritical holomorphic functions on Stein spaces. J. Eur. Math. Soc. (JEMS), 18(11):2511-2543, 2016. MR 3562350 Zbl 1359.32011 arXiv
Embedded minimal surfaces in Rⁿ (with A. Alarcón and F. J. López). Math. Z., 283(1):1-24, 2016. Full text view only. MR 3489056 Zbl 1360.53020 arXiv
On the Hodge conjecture for q-complete manifolds (with J. Smrekar and A. Sukhov). Geom. & Topol., 20(1):353-388, 2016. MR 3470716 Zbl 06553431 arXiv
Minimal hulls of compact sets in R³ (with B. Drinovec Drnovšek). Trans. Amer. Math. Soc., 368(10):7477-7506, 2016. MR 3471098 Zbl 1339.53004 arXiv
Every bordered Riemann surface is a complete conformal minimal surface bounded by Jordan curves (with A. Alarcón, B. Drinovec Drnovšek, and F. J. López). Proc. London Math. Soc. (3), 111(4):851-886, 2015. MR 3407187 Zbl 1344.53008 arXiv
Null holomorphic curves in ℂ³ and the conformal Calabi-Yau problem (with A. Alarcón). In: Complex Geometry and Dynamics, 101-121, Abel Symp., 10, Springer, Cham, 2015. PDF MR 3587463 Zbl 1338.53085 arXiv
The Calabi-Yau problem, null curves, and Bryant surfaces (with A. Alarcón). Math. Ann. 363(3-4):913-951, 2015. MR 3412347 Zbl 1343.53053 arXiv
Fatou-Bieberbach domains in ℂⁿ\R^k (with E. F. Wold). Ark. Mat., 53(2):259-270, 2015. MR 3391171 Zbl 1333.32015 arXiv
A complex surface admitting a strongly plurisubharmonic function but no holomorphic functions. J. Geom. Anal., 25(1):329-335, 2015. MR 3299284 Zbl 1317.32020 arXiv

Publications 1986-2014. These files are provided for non-commercial, personal, academic use of individual researchers. Any other use requires explicit permission from the publisher since the papers are protected by copyright.

Gromov's contribution to the Oka principle. In: A few snapshots from the work of Mikhail Gromov. The Abel Prize 2008-2012, pp. 161-165. Edited by Helge Holden and Ragni Piene. Springer, Heidelberg, 2014. PDF MR 3185030 Zbl 1317.01017
Holomorphic flexibility properties of compact complex surfaces (with F. Lárusson). Int. Math. Res. Not. (IMRN), 13:3714-3734, 2014. PDF MR 3229766 Zbl 1310.32013 arXiv
Oka properties of groups of holomorphic and algebraic automorphisms of complex affine space (with F. Lárusson). Math. Res. Lett. 21(5):1047-1067, 2014. PDF MR 3294562 Zbl 1306.32009 arXiv
Oka properties of ball complements (with T. Ritter). Math. Z., 277(1):325-338, 2014. PDF MR 3205776 Zbl 1297.32010 arXiv Notice: proofs of Theorem 1, Corollary 2 and Theorem 15 are incomplete in the special case when the set L is polynomially convex and the real dimension of X equals n. These proofs can be completed by applying Lemma 3.1 in the paper Proper holomorphic immersions into Stein manifolds with the density property. J. Anal. Math., 139:2 (2019), 585-596. On the same subject, a recent result of Y. Kusakabe (May 2020) is that complements of polynomially convex sets in complex Euclidean spaces of dimension at least two are Oka manifolds; see arXiv and also the paper Holomorphic families of Fatou-Bieberbach domains and applications to Oka manifolds by E. Fornæss Wold and myself.
Null curves and directed immersions of open Riemann surfaces (with A. Alarcón). Invent. Math., 196(3):733-771, 2014. PDF MR 3211044 Zbl 1297.32009 arXiv
Oka manifolds: from Oka to Stein and back. With an appendix by F. Lárusson. Ann. Fac. Sci. Toulouse Math. (6), 22(4):747-809, 2013. PDF MR 3137250 Zbl 1323.32001 arXiv
Every bordered Riemann surface is a complete proper curve in a ball (with A. Alarcón). Math. Ann. 357(3):1049-1070, 2013. PDF MR 3118624 Zbl 1288.32014 arXiv
Gunning-Narasimhan's theorem with a growth condition (with T. Ohsawa). J. Geom. Anal. 23(3):1078-1084, 2013. PDF MR 3078344 Zbl 1272.30065 arXiv Japanese translation
Embeddings of infinitely connected planar domains into ℂ² (with E. F. Wold). Analysis & PDE 6(2): 499-514, 2013. PDF MR 3071396 Zbl 1277.32009 arXiv
Characterizations of projective hulls by analytic discs (with B. Drinovec Drnovšek). Illinois J. Math. 56:1 (2012) 53-65 (2013). PDF MR 3117017 Zbl 1311.32013 arXiv
The Poletsky-Rosay theorem on singular complex spaces (with B. Drinovec Drnovšek). Indiana Univ. Math. J. 61 (2012) 1707-1423. PDF MR 3085613 Zbl 1278.32021 arXiv
Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties (with B. Drinovec Drnovšek). Ann. Polon. Math. 106 (2012) 171-191. PDF MR 2995450 Zbl 1258.32011 arXiv
Holomorphic families of long ℂ²'s. Proc. Amer. Math. Soc. 140 (2012) 2383-2389. PDF MR 2898700 Zbl 1278.32012 arXiv
Survey of Oka theory (with F. Lárusson). New York J. Math., 17a (2011), 1-28. PDF MR 2782726 Zbl 1225.32019
Invariance of the parametric Oka property. Complex Analysis, 125-144. Trends in Math., Birkhäuser (2010). PDF MR 2885112 Zbl 1208.32012 arXiv >
The Oka principle for sections of stratified fiber bundles. Pure Appl. Math. Quarterly 6 (2010) 843-874. PDF MR 2677316 Zbl 1216.32005 arXiv >
Strongly pseudoconvex Stein domains as subvarieties of complex manifolds (with B. Drinovec Drnovšek). Amer. J. Math. 132 (2010) 331-360. PDF MR 2654777 Zbl 1216.32009 arXiv >
Oka Maps. C. R. Acad. Sci. Paris Ser. I 348 (2010) 145-148. PDF MR 2600066 Zbl 1201.32013 arXiv >
Fibrations and Stein neighborhoods (with E.F. Wold). Proc. Amer. Math. Soc. 138 (2010) 2037-2042. PDF MR 2596039 Zbl 1192.32008 arXiv >
Abelova nagrada 2009 Mikhaelu Gromovu. (Slovenian) (The Abel prize 2009 to Mikhael Gromov.) Obzornik mat. fiz. 57 (2010) 2, 41-52. PDF MR 2677126 Zbl 1205.01033
Princip Oka-Grauert-Gromov in uporaba v kompleksni geometriji. (Slovenian; The Oka-Grauert principle and its applications in complex geometry). Unpublished, University of Ljubljana (2010). PDF
Oka Manifolds. C. R. Acad. Sci. Paris, Ser. I 347 (2009) 1017-1020. PDF MR 2554568 Zbl 1175.32005
Bordered Riemann surfaces in ℂ² (with E. F. Wold). J. Math. Pures Appl. 91 (2009) 100-114. PDF MR 2487902 Zbl 1157.32010
Approximation of holomorphic mappings on strongly pseudoconvex domains (with B. Drinovec Drnovšek). Forum Math. 20 (2008) 817-840. PDF MR 2445119 Zbl 1155.32008
Stein compacts in Levi-flat hypersurfaces (with C. Laurent-Thiébaut). Trans. Amer. Math. Soc. 360 (2008) 307-329. PDF MR 2342004 Zbl 1141.32003
Holomorphic curves in complex spaces (with B. Drinovec Drnovšek). Duke Math. J. 139 (2007) 203-254. PDF MR 2352132 Zbl 1133.32002
Deformations of Stein structures and extensions of holomorphic mappings (with M. Slapar). Math. Res. Lett. 14 (2007) 343-357. PDF MR 2318630 Zbl 1134.32007
An interpolation theorem for proper holomorphic embeddings (with B. Ivarsson, F. Kutzschebauch and J. Prezelj). Math. Ann. 338 (2007) 545-554. PDF MR 2317930 Zbl 1177.32003
Manifolds of holomorphic mappings from strongly pseudoconvex domains. Asian J. Math. 11 (2007) 113-126. PDF MR 2304585 Zbl 1131.58007
Stein structures and holomorphic mappings (with M. Slapar). Math. Z. 256 (2007) 615-646. PDF MR 2299574 Zbl 1129.32013
A contractible Levi-flat hypersurface in ℂ² which is a determining set for pluriharmonic functions. Ark. Math. 44 (2006) 87-91 PDF MR 2237212 Zbl 1158.32314
Runge approximation on convex sets implies Oka's property. Ann. of Math. (2) 163 (2006) 689-707. PDF MR 2199229 Zbl 1103.32004
Holomorphic flexibility properties of complex manifolds. Amer. J. Math. 128 (2006) 239-270. PDF MR 2197073 Zbl 1171.32303
Holomorphic discs with dense images (with J. Winkelmann). Math. Res. Lett. 12 (2005) 265-268. PDF MR 2150882 Zbl 1075.32005
Extending holomorphic mappings from subvarieties in Stein manifolds. Ann. Inst. Fourier 55 (2005) 733-751. PDF MR 2149401 Zbl 1076.32003
Holomorphic submersions from Stein manifolds. Ann. Inst. Fourier 54 (2004) 1913-1942. PDF MR 2134229 Zbl 1093.32003
Most real analytic Cauchy-Riemann manifolds are nonalgebraizable. Manuscripta Math. 115 (2004) 489-494. PDF MR 2103663 Zbl 1066.32034
Noncritical holomorphic functions on Stein manifolds. Acta Math. 191 (2003) 143-189. PDF MR 2051397 Zbl 1064.32021
Strongly pseudoconvex handlebodies (with J. Kozak). J. Korean Math. Soc. 40 (2003) 727-745. PDF MR 1995074 Zbl 1044.32025
Stein domains in complex surfaces. J. Geom. Anal. 13 (2003) 77-94. PDF MR 1967038 Zbl 1039.32013
The Oka principle for multivalued sections of ramified mappings. Forum Math. 15 (2003) 309-328. PDF MR 1956971 Zbl 1023.32007
The homotopy principle in complex analysis: A survey. In: Explorations in Complex and Riemannian Geometry, 73-99; Contemp. Math., 332, Amer. Math. Soc., Providence, RI (2003). PDF MR 2016091 Zbl 1048.32004 arXiv >
Embedding some bordered Riemann surfaces in the affine plane (with M. Černe). Math. Res. Lett. 9 (2002) 683-696. PDF MR 1906070 Zbl 1030.32013
The Oka principle for sections of subelliptic submersions. Math. Z. 241 (2002) 527-551. PDF MR 1938703 Zbl 1023.32008
Oka's principle for holomorphic submersions with sprays (with J. Prezelj). Math. Ann. 322 (2002) 633-666. PDF MR 1905108 Zbl 1011.32006
Solving the d- and dibar-equations in thin tubes and applications to mappings (with E. Løw and N. Øvrelid). Michigan Math. J. 49 (2001) 369-416. PDF MR 1852309 Zbl 1016.32018
Proper holomorphic discs in ℂ² (with J. Globevnik) Math. Res. Lett. 8 (2001) 257-274. PDF MR 1839476 Zbl 1027.32018
On complete intersections. Ann. Inst. Fourier 51 (2001) 497-512. PDF MR 1824962 Zbl 0991.32008
Extending holomorphic sections from complex subvarieties (with J. Prezelj). Math. Z. 236 (2001) 43-68. PDF MR 1812449 Zbl 0968.32005
An interpolation theorem for holomorphic automorphisms of ℂⁿ (with G. Buzzard). J. Geom. Anal. 10 (2000) 101-108. PDF MR 1758584 Zbl 0963.32014
Oka's principle for holomorphic fiber bundles with sprays (with J. Prezelj). Math. Ann. 317 (2000) 117-154. PDF MR 1760671 Zbl 0964.32017
Interpolation by holomorphic automorphisms and embeddings in ℂⁿ. J. Geom. Anal. 9 (1999) 93-118. PDF MR 1760722 Zbl 0963.32006
Holomorphic equivalence of smooth submanifolds in ℂⁿ (with E. Løw). Indiana Univ. Math. J. 46 (1997) 133-153. PDF MR 0883.32014 Zbl 0883.32014
A Carleman type theorem for proper holomorphic embeddings (with G. Buzzard). Ark. Mat. 35 (1997) 157-169. PDF MR 1443039 Zbl 0886.32014
Actions of (R,+) and (C,+) on complex manifolds. Math. Z. 223 (1996) 123-153. PDF MR 1408866 Zbl 0872.32021
Embedding holomorphic discs through discrete sets (with J. Globevnik and B. Stensønes). Math. Ann. 305 (1996) 559-569. PDF MR1397436 Zbl 0859.32010
Non straightenable complex lines in ℂ² (with J. Globevnik and J.-P. Rosay). Ark. Mat. 34 (1996) 97-101. PDF MR 1396625 Zbl 0853.58015
Flows on ℂ² with polynomial time one map (with P. Ahern and D. Varolin). Complex Var. Theory Appl. 29 (1996) 363-366. PDF MR1390620 Zbl 0854.32018
Holomorphic automorphisms of ℂⁿ: A survey. In: Complex Analysis and Geometry (Trento, 1993), 173-199; Lecture Notes in Pure and Appl. Math., 173, Dekker, New York (1996). PDF MR 1365974 Zbl 0849.32022
A theorem in complex symplectic geometry. J. Geom. Anal. 5 (1995) 379-393. PDF MR 1360826 Zbl 0836.58015
Limits of complete holomorphic vector fields. Math. Res. Lett. 2 (1995) 401-414. PDF MR 1355704 Zbl 0859.32006
One parameter automorphism groups on ℂ² (with P. Ahern). Complex Var. Theory Appl. 27 (1995) 245-268. PDF MR 1333980 Zbl 1278.32021
Equivalence of real submanifolds under volume preserving holomorphic automorphisms of ℂⁿ. Duke Math. J. 77 (1995) 431-445. PDF MR1321065 Zbl 0831.32009
Approximation by automorphisms on smooth submanifolds of ℂⁿ. Math. Ann. 300 (1994) 719-738. PDF MR 1314745 Zbl 0821.32028
Complements of Runge domains and holomorphic hulls. Michigan Math. J. 41 (1994) 297-308. PDF MR 1278436 Zbl 0811.32007
Intersections of totally real and holomorphic discs (with T. Duchamp). Publ. Mat. 37 (1993) 3-17. PDF MR 1240927 Zbl 0808.32022
A reflection principle on strongly pseudoconvex domains with generic corners. Math. Z. 213 (1993) 49-64. PDF MR 1217670 Zbl 0790.32024
Approximation of biholomorphic mappings by automorphisms of ℂⁿ (with J.-P. Rosay). Invent. Math. 112 (1993) 323-349. PDF MR1213106 Zbl 0792.32011 Erratum: Invent. Math. 118 (1994) 573-574. PDF MR 1296357 Zbl 0808.32017
Proper holomorphic mappings: a survey. In: Several complex variables, Mittag-Leffler Institute (Stockholm, 1987-88), 297-363; Math. Notes, 38, Princeton Univ. Press, Princeton, NJ (1993). PDF MR 1207867 Zbl 0778.32008
Intersections of analytic and smooth discs. In: The Madison Symposium on Complex Analysis, Madison, Wisconsin, 1991, pp. 235-244. Contemp. Math. 137. Amer. Math. Soc., Providence (1992) PDF MR 1190985 Zbl 0768.32005
Complex tangents of real surfaces in complex surfaces. Duke Math. J. 67 (1992) 353-376. PDF MR 1177310 Zbl 0761.53032
The length of a set in the sphere whose polynomial hull contains the origin. Indag. Math. (N.S.) 3 (1992) 169-172. PDF MR 1168343 Zbl 0762.32007
An elementary proof of Fefferman's theorem. Expo. Math. 10 (1992) 135-150. PDF MR 1164529 Zbl 0759.32018
Discs in pseudoconvex domains (with J. Globevnik). Comment. Math. Helv. 67 (1992) 129-145. PDF MR 1144617 Zbl 0779.32016
Mappings of quadric Cauchy-Riemann manifolds. Math. Ann. 292 (1992) 163-180. PDF MR 1141791 Zbl 0749.32006
A smooth holomorphically convex disc in ℂ² that is not locally rationally convex. Proc. Amer. Math. Soc. 116 (1992) 411-415. PDF MR 1101982 Zbl 1278.32021
Admissible boundary values of bounded holomorphic functions in wedges. Trans. Amer. Math. Soc. 332 (1992) 583-593. PDF MR 1087055 Zbl 1278.32021
Mappings of strongly pseudoconvex Cauchy-Riemann manifolds. Several complex variables and complex geometry, Santa Cruz, 1989, Proc. Symp. Pure Math. 52, Part 1, 59-92. Amer. Math. Soc., Providence (1991). PDF MR 1128516 Zbl 0739.32022
A new class of polynomially convex sets in ℂ² (with E. L. Stout). Ark. Mat. 29 (1991) 51-62. PDF MR 1115074 Zbl :0734.32006
A totally real three-sphere in ℂ³ bounding a family of analytic discs. Proc. Amer. Math. Soc. 108 (1990) 887-892. PDF MR 1038758 Zbl 0688.32016
Extending proper holomorphic mappings of positive codimension. Invent. Math. 95 (1989) 31-62. PDF MR 0969413 Zbl 0633.32017
Polynomial hulls of sets fibered over the circle. Indiana Univ. Math. J. 37 (1988) 869-889. PDF MR 0982834 Zbl 0647.32017
Regularity of varieties in strictly pseudoconvex domains. Publ. Mat. 32 (1988) 145-150. PDF MR 0939779 Zbl 0737.32008
Localization of the Kobayashi metric and the boundary continuity of proper holomorphic mappings (with J.-P. Rosay). Math. Ann. 279 (1987) 239-252. PDF MR 0919504 Zbl 0644.32013
Analytic disks with boundaries in a maximal real submanifold of ℂ². Ann. Inst. Fourier 37 (1987) 1-44. PDF MR 0894560 Zbl 0583.32038
On totally real embeddings into ℂⁿ. Exposition. Math. 4 (1986) 243-255. PDF MR 0880125 Zbl 0597.57018
Polynomially convex hulls with piecewise smooth boundaries. Math. Ann. 276 (1986) 97-104. PDF MR 0863710 Zbl 0585.32016
On the boundary regularity of proper holomorphic mappings. Ann. Sc. Norm. Sup. Pisa Cl. Sci. (4) 13 (1986) 109-128. PDF MR 0863637 Zbl 0605.32011
Proper holomorphic maps from balls. Duke Math. J. 53 (1986) 427-441. PDF MR 0850544 Zbl 0603.32019
Embedding strictly pseudoconvex domains into balls. Trans. Amer. Math. Soc. 295 (1986) 347-368. PDF MR 0831203 Zbl 0594.32024
Some totally real embeddings of three-manifolds. Manuscripta Math. 55 (1986) 1-7. PDF MR 0828408 Zbl 0586.32027
Stability of polynomial convexity of totally real sets. Proc. Amer. Math. Soc. 96 (1986) 489-494. PDF MR 0822446 Zbl 0588.32016

Articles in Slovenian

Akad. Prof. dr. Josip Globevnik, novi častni član DMFA Slovenije. Obzornik mat. fiz. 68(3):112-113, 2021.
Matematika in razvoj osebnosti
Kam želijo slovenske Univerze
Visoko šolstvo in tržna ekonomija
Razvoj slovenskega visokošolskega prostora

Lectures at international conferences, 2010-

Runge and Mergelyan theorems on families of open Riemann surfaces. SCV and complex geometry conference dedicated to the mathematical work of Yum--Tong Siu, Academia Sinica, Taipei, 6-10 January 2025.
Isotopies of complete minimal surfaces of finite total curvature. Conference Geometric Methods of Complex Analysis, Bergische Univesität Wuppertal, 21-25 October 2024
New developments in Oka theory. Giornata INdAM 2024. Riemann International School of Mathematics, Villa Toeplitz, Varese, 2 October 2024
The minimal metric on domains in real Euclidean spaces. Invariant metrics in complex analysis. Villa Mondragone, Frascati, 18 - 20 September 2024
Oka tubes in holomorphic line bundles. Recent developments on the d-bar equation. SCV conference 2024, remembering Nils Øvrelid. University of Oslo, 8 - 10 August 2024
Minimal surfaces with symmetries. CR Geometry and PDEs X. Levico Terme, Italy, 27 - 30 May 2024
Oka tubes in holomorphic line bundles. Analysis and Geometry in Several Complex Variables. Erwin Schrödinger Institute, Vienna, 20 - 24 November 2023
Oka-1 manifolds. Complex analysis and geometry: celebrating the 70+1th birthday of László Lempert. Rényi Institute, Budapest, 26 June - 30 June 2023
Oka-1 manifolds. Oka Theory and Complex Geometry Conference, Sophus Lie Center, Nordfjordeid (Norway), 19 - 23 June 2023
Proper holomorphic embeddings: from classical to recent. SCV Oslo Conference 2022, marking the retirement of Erik Løw. University of Oslo, 1 - 3 December 2022
Oka domains in Euclidean and projective spaces. Fifth Central European Complex Analysis Meeting, Drnholec, Czech Republic, 4 - 6 November 2022
New developments on Oka manifolds. Complex Geometry Workshop, Ruhr University Bochum, 9 - 13 September 2022
Oka domains in Euclidean and projective spaces. Complex Analysis and Geometry - XXVI, Levico Terme (Trento, Italy), 19 - 23 September 2022
Oka domains in Euclidean spaces. CR Geometry and PDE's IX, Levico Terme (Trento, Italy), 30 May - 2 June 2022
Euclidean domains in complex manifolds. The Conference on Complex Geometric Analysis in honor of Kang-Tae Kim's 65th birthday, POSTECH, Pohang, Korea, 11 - 14 January 2022
Hyperbolic domains in real Euclidean spaces. Complex Analysis and Geometry, Ufa, Russia, 16 - 19 November 2021
Hyperbolic domains in real Euclidean spaces. International Conference on Complex Analysis Dedicated to the Memory of Andrei Gonchar and Anatoliy Vitushkin, Steklov Mathematical Institute, Moscow, 11-15 October 2021
Minimal surfaces from a complex analytic viewpoint. Plenary lecture, 8th European Congress of Mathematics, Portorož, Slovenia, 20-25 June 2021
Schwarz-Pick lemma for harmonic maps which are conformal at a point. Geometric Methods of Complex Analysis, Oberwolfach, 16-22 May 2021
Mergelyan's and Arakelian's theorems for manifold-valued maps. 27th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (ICFIDCAA), Krasnoyarsk, 11-15 August 2019
H-principle for complex contact structures on Stein manifolds. Analysis and CR geometry, ESI - Vienna, Austria, 10-14 December 2018
Runge tubes. Holomorphic Elliptic Geometry and Group Actions, University of Bern, Switzerland, 5-7 September 2018
Runge tubes. Hayama Symposium on Several Complex Variables XX joint with Pacific Rim Complex-Symplectic Geometry conference, Shonan Village Center, Hayama, Japan, 13-17 July 2018
New developments in nonlinear holomorphic approximation theory. CR-Geometry and PDE's-VIII, Levico Terme, Trento, Italy, 4-8 June 2018
Nonlinear holomorphic approximation theory. Complex Analysis and Related Topics, Euler International Mathematical Institute, St. Petersburg, 23-27 April 2018
Runge tubes. Second Central European Complex Analysis Meeting, University of Vienna, Austria, 12-14 April 2018
A properly embedded holomorphic disc in the ball with finite area and dense boundary curve. Complex Geometry for Serguei Ivashkovych's 60th anniversary, Lille, 23-24 November 2017
Proper holomorphic embeddings and immersions into Stein manifolds with the density property. International Conference on Complex Analysis Dedicated to the memory of Andrei Gonchar and Anatoliy Vitushkin, Steklov Mathematical Institute, Moscow, 9-10 October 2017
Divisors defined by noncritical functions. Workshop on ∂ at NTNU Trondheim, Norway, 5-8 October 2017
Proper holomorphic mappings of Stein manifolds. Festkolloquium Anlässlich des 80. Geburtstags von Otto Forster, Ludwig Maximilians-Universität München, 14 July 2017
Holomorphic immersions and embeddings of Stein manifolds into Stein manifolds with the density property. The KSCV12 Symposium; The 12th Korean Conference on Several Complex Variables - in honor of Kang-Tae Kim's 60th birthday, The Kolon Hotel in Gyeong-Ju, South Korea, 3-7 July 2017
Holomorphic Legendrian curves and Darboux charts. Complex Analysis and Geometry - XXIII, Levico Terme (Trento), Italy, 11-15 June 2017
Holomorphic Legendrian curves. Conference on Complex Geometry, Dynamical Systems and Foliation Theory, Institute for Mathematical Sciences, National University of Singapore, 15-19 May 2017
Complete bounded submanifolds in different geometries. Workshop su varietà reali e complesse: geometria, topologia e analisi armonica, Scuola Normale Superiore, Palazzo della Carovana, Pisa, Italy, 24-26 February 2017
New complex analytic methods in the study of non-orientable minimal surfaces in Rⁿ. The INdAM Workshop Complex function theory, its generalizations and applications, Rome, Italy, 12-16 September 2016
A long C² without holomorphic functions. CR Geometry and PDE's - VII, dedicated to the memory of Giuseppe Zampieri, Levico Terme (Trento), Italy, 26 June - 1 July 2016
Every meromorphic function is the Gauss map of a conformal minimal surface. INdAM Meeting Complex and Symplectic Geometry, Cortona, Italy, 13-17 June 2016
The h-principle for minimal surfaces in Rⁿ and null curves in Cⁿ. Complex Analysis and Complex Geometry, Banff International Research Station, Banff, Canada, 1-6 May 2016
Non-orientable minimal surfaces in Rⁿ. Several complex variables and CR geometry, Erwin Schrödinger Institute, Vienna, Austria, 3-13 November 2015
Minimal surfaces in minimally convex domains. The Eighth Workshop on Geometric Analysis of PDEs and Several Complex Variables, Serra Negra, Sāo Paulo, Brazil, 3-7 August 2015
Minimal surfaces in minimally convex domains. Complex Analysis and Geometry - XXII, Levico Terme, Italy, 1-5 June 2015
Complete conformal minimal surfaces with Jordan boundaries in Rⁿ. NORDAN 2015, University of Iceland, Reykjavik, Iceland, 25-26 April 2015
Minimal hulls of compact sets in R³. Norwegian-Spanish Workshop in Complex Variables and Applications, Complutense University of Madrid, Spain, 19-20 February 2015
Minimal hulls of compact sets in R³. Geometric Methods of Complex Analysis, Mathematisches Forschungsinstitut Oberwolfach, Germany, 25-31 January 2015
Noncritical holomorphic functions on Stein spaces. Analysis and geometry in several complex variables, Texas A&M University at Qatar, Doha, Qatar, 4-8 January 2015
The Oka-Grauert principle: its first 75 years (plenary lecture). Gedenkkolloquium für Hans Grauert, University of Bonn, Germany, 27 June 2014
The Hodge conjecture for q-complete manifolds. CR Geometry and PDE's - VI, Levico Terme, Italy, 23-27 June 2014
Complex analysis and the conformal Calabi-Yau problem. Abel Symposium 2013, Trondheim, Norway, 2-5 July 2013
The conformal Calabi-Yau problem. Complex Analysis and Geometry - XXI, Levico Terme (Trento), Italy, 2-7 June 2013
Null-curves and directed immersions of Riemann surfaces. Workshop Geometric and Complex Analysis, Granada, Spain, 22-23 November 2012
Every bordered Riemann surface is a complete proper curve in a ball. Geometric Methods in Several Complex Variables, Lille, France, 25-26 October 2012
Embeddings of infinitely connected planar domains into ℂ². Conference on CR Geometry and PDE's - V, Levico Terme, Trento, Italy, 5-8 June 2012
Two theorems on Riemann surfaces. Workshop in several complex variables, University of Amsterdam, The Netherlands, 12-16 December 2011
What is an Oka manifold? Plenary lecture, OeMG-Tagung - CSASC 2011, Krems, Austria, 25-28 September 2011.
The Poletsky-Rosay theorem on singular complex spaces. Conference on Several Complex Variables on the occasion of Professor Józef Siciak's 80th birthday, Jagielonnian University, Krakow, Poland, 4-8 July 2011
The Poletsky-Rosay theorem on singular complex spaces. Southern California Analysis and PDE Conference, U.C. San Diego, California, 28-29 May 2011
Embedding Riemann surfaces in ℂ². Almost complex geometry and foliations, Lille, France, 23-29 May 2010
Recent advances in elliptic complex geometry. Recent Advances in Function Related Operator Theory, Rincón, Puerto Rico, 22-26 March 2010

Lectures at international schools

Applications of complex analysis to minimal surfaces. Partial Differential Equations in Complex Geometry and Singular Spaces, American University in Beirut, 24-27 November 2014. Lecture 1 Lecture 2 Lecture 3
Oka Manifolds. Komplex Analysis Winter School KAWA4, Toulouse, France, 21-24 January 2013. Lecture Notes
Non-singular holomorphic foliations on Stein manifolds. Foliations, pseudoholomorphic curves, applications, Institut Fourier, University of Grenoble, France, 18 June - 6 July 2012
Noncritical holomorphic functions on Stein manifolds. Variétés complexes et feuilletages, IRMA Strasbourg, France, 7-10 June 2010

Organization of international conferences and PhD schools

Complex Analysis, Geometry, and Dynamics III - Portorož 2024, Hotel Histrion, Portoro�, Slovenia, 10 -14 June 2024
Complex Analysis, Geometry, and Dynamics II - Portorož 2023, Hotel Histrion, Portoro�, Slovenia, 5 - 9 June 2023
Complex Analysis, Geometry, and Dynamics - Portorož 2022, Hotel Bernardin, Portoro�, Slovenia, 20 - 24 June 2022
Frontiers in Elliptic Holomorphic Geometry, Jevnaker, Norway, 10-14 October 2016
Workshop in Complex Analysis - Ljubljana 2016, FMF and IMFM, Ljubljana, Slovenia, 24-26 March 2016
Sanya School in Complex Analysis and Geometry, Tsinghua Sanya International Mathematics Forum (TSIMF), Sanya, China, 11-20 January 2016
Complex Analysis, Geometry and Dynamics - School and Workshop, International Centre for Theoretical Physics (ICTP), Trieste, Italy, 21 September - 3 October 2015
International Conference on Complex Geometry and Several Complex Variables, East China Normal University, Shanghai, China, 11-15 May 2015
Several Complex Variables Symposium, Tsinghua Sanya International Mathematics Forum (TSIMF), Sanya, China, 12-16 May 2014
Minisymposium on Several Complex Variables, CSASC, Primorska University, Koper, Slovenia, 10-12 June 2013
Workshop Geometric and Complex Analysis, Granada, Spain, 22-23 November 2012
Several Complex Variables - Ljubljana 2012, University of Ljubljana, Slovenia, 27-29 September 2012
Minisymposium on Complex Analysis, OeMG-Tagung - CSASC 2011, University of Krems, Austria, 25-28 September 2011
Member of the Scientific Committee of KAWA (a series of PhD schools and conferences), 2009-2016
Several Complex Variables and Connections with PDEs and Geometry, Fribourg, Switzerland, 7-11 July 2008
The International Summer School in Several Complex Variables, Szczyrk, Poland, 19-23 June 2006
A Symposium in Complex Analysis - Slovenia 2006, Kranjska Gora, Slovenia, 7-10 June 2006
Conference on Complex Analysis}, University of Wisconsin, Madison, USA, 16-19 March 2006
Seattle Symposium on Complex Analysis, University of Washington, Seattle, USA, March 1998
Geometric and analytic methods in several complex variables (Special session), AMS regional meeting, Iowa City, USA, March 1996
Midwest several complex variables seminar, University of Wisconsin, Madison, USA, April 1995

Beamer files of lectures:

Minimal surfaces from a complex analytic viewpoint. Kyushu University, Fukuoka, 5 September 2024.
Oka manifolds and their role in complex analysis and geometry. University of Oxford, 7 May 2024. Slides.
Recent developments on Oka manifolds. University of Berne, 22 May 2023
Oka manifolds. Masaryk University of Brno, 4 - 6 April 2023. Lecture 1 Lecture 2 Lecture 3
Hyperbolic domains in real Euclidean spaces. University of Granada, 1 April 2022
Mergelyan approximation theorem for holomorphic Legendrian curves. University of Ljubljana, 25 February 2020
The Calabi-Yau problem for minimal surfaces of finite genus and countably many ends. University of Ljubljana, 7 January 2020
Runge tubes. Geometria Complessa e Geometria Differenziale, Università degli Studi di Firenze, Italia, 24 Maggio 2018
Runge tubes. Istanbul Analysis Seminars, Sabanci University, Istanbul, Turkey, 16 March 2018
A properly embedded holomorphic disc in the ball with finite area and dense boundary curve. Geometry Seminar, University of Granada, Spain, 9 February 2018
Holomorphic Legendrian curves. Differential Geometry Seminar, University of Adelaide, 26 May 2017
Complete bounded submanifolds in different geometries. Dublin Mathematics Colloquium, Trinity College, Dublin, 30 March 2017
Every meromorphic function is the Gauss map of a conformal minimal surface. Geometry Seminar, University of Granada, Spain, 27 January 2017
Every meromorphic function is the Gauss map of a conformal minimal surface. Center for Advanced Study, Oslo, 17 November 2016
The h-principle for minimal surfaces and null curves. Geometry Seminar, University of Granada, Spain, 18 March 2016
A long C² without holomorphic functions. Differential Geometry Seminar, University of Adelaide, 29 January 2016.
Oka manifolds and minimal surfaces. Geometry Seminar, University of Granada, Spain, 13 November 2015

Lectures at international schools:

The Beirut Lectures on minimal surfaces, AUB, Beirut, Lebanon, 2014: Lecture 1 Lecture 2 Lecture 3
Oka Manifolds. Lectures at KAWA 4, Toulouse, France, 2013.

Lecture notes for some of my courses (in Slovenian):

Analiza na mnogoterostih
Riemannove ploskve
Kompleksna analiza
Analiza 4: Uvod v parcialne diferencialne enačbe
Dinamični sistemi
Zveza med Chernovo ukrivljenostjo in q-konveksnostjo

prof. dr. Franc Forstnerič

CV Biografija Publications MathSciNet Zentralblatt arXiv CRIS ORCID ScholarGPS GoogleScholar

Complex Analysis, Geometry, and Dynamics IV - Portorož 2025, 16-20 June 2025

International Journal of Mathematics, member of the editorial board

Complex Analysis Seminar, 1975-

Research interests and grants

ERC Advanced Grant, 101053085 - Holomorphic partial differential relations, 2023-2027

Plenary speaker, 8th European Congress of Mathematics, Portorož, 20-25 June 2021. Slides

Stefan Bergman Prize 2019 Obzornik mat. fiz. 68(2):74-81, 2021

Complex Analysis, Geometry, and Dynamics III - Portorož 2024, 10-14 June 2024

Complex Analysis, Geometry, and Dynamics II - Portorož 2023, 5-9 June 2023

Complex Analysis, Geometry and Dynamics - Portorož 2022, 20-24 June 2022

Stein Manifolds and Holomorphic Mappings 2018, Ljubljana, 17-21 September 2018 Photos

Books

Preprints

Online first publications

Research and expository papers, 2015-2024

Publications 1986-2014. These files are provided for non-commercial, personal, academic use of individual researchers. Any other use requires explicit permission from the publisher since the papers are protected by copyright.

Articles in Slovenian

Lectures at international conferences, 2010-

Lectures at international schools

Organization of international conferences and PhD schools

Beamer files of lectures:

Lectures at international schools:

Lecture notes for some of my courses (in Slovenian):

A few of my favorite places

Eva's art

Events