Franc Forstnerič

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Franc Forstnerič (born May 1, 1958 in Ljubljana ) is a Slovenian mathematician and professor at the University of Ljubljana . He deals with complex analysis in multiple variables and geometry.

Career

Forstneric studied mathematics at the University of Ljubljana with a degree in 1980 and received his PhD under Edgar Lee Stout (Proper Holomorphic Mappings in Several Complex Variables) at the University of Washington in Seattle in 1985 , where he was a Fulbright scholar . In 1986 he became an Assistant Professor and in 1989 an Associate Professor in Ljubljana. From 1991 to 1993 (and previously in 1988) he was visiting professor at the University of Wisconsin-Madison , where he became an associate professor with tenure in 1993 and a full professorship in 1994. He also received a full professorship in Ljubljana in 1994 (in absentia). From 2007 to 2009 and 2011 to 2013 he was dean of the Faculty of Mathematics and Physics in Ljubljana.

He was visiting scholar and visiting professor at the University of Provence in Marseille (1986), at the Mittag-Leffler Institute (1987/88), at the Max Planck Institute for Mathematics in Bonn (1990), at the University of Lille (1994), Rom-Tor Vergata (2007), Bern (2007), at the Center for Advanced Study in Oslo (2016), at Stanford University (2019), at the University of Adelaide and the University of Granada.

plant

In complex analysis in the 1980s, he initially dealt with holomorphic mappings between areas, their regularity on boundaries and their extensions. He constructed really-holomorphic embeddings of strongly-pseudoconvex regions in balls and proved that every really-holomorphic mapping between balls that is sufficiently regular at the edge is rational. He also began studying group-invariant holomorphic mappings of balls, which was the starting point for the study of holomorphic mappings (existential questions, regularity, classification) between areas of different dimensions. In the 1990s he dealt with Andersén-Lémpert theory, which deals with automorphisms between complex Euclidean vector spaces and some other complex manifolds with flows of complete holomorphic vector fields. He also dealt with the modern extensions of the Oka-Grauert principle, initiated in 1989 by Michail Leonidowitsch Gromow . At first he worked with his doctoral student Jasna Prezelj. In this context, he introduced a new class of so-called Oka manifolds in 2009 , which, in a precise homotopy -theoretical sense, are dual to Stein manifolds and a counterpart to hyperbolic manifolds. He published a monograph on this in 2011. He also constructed non-critical holomorphic functions on stone manifolds and spaces.

From 2012 he dealt with the theory of minimal surfaces in Euclidean spaces. He worked with Antonio Alarcón and Francisco J. López from the University of Granada, among other things in the approximation theory and homotopy theory of minimal surfaces. In doing so, they also made significant progress on the Calabi-Yau problem for minimal areas. They showed that every Riemann surface of finite gender with at most a countable number of boundary curves has the conformal structure of a restricted complete minimal surface in the Jordan curve boundary. In addition to Euclidean spaces, the techniques were also used in holomorphic contact geometries.

Honors and memberships

In 1988 he received the Boris Kridric Prize of the Republic of Slovenia. In 2019 he received the Stefan Bergman Prize from the American Mathematical Society . For 2020/21 he was selected as plenary speaker at the 8th ECM .

In 1999 he became an associate and in 2005 a full member of the Slovenian Academy of Sciences.

Fonts (selection)

  • Embedding strictly pseudoconvex domains into balls , Transactions of the American Mathematical Society, Volume 295, 1986, pp. 347-368
  • Proper holomorphic maps from balls , Duke Mathematical Journal, Volume 53, 1986, pp. 427-441
  • with JP Rosay: Localization of the Kobayashi metric and the boundary continuity of proper holomorphic mappings , Mathematische Annalen, Volume 279, 1987, pp. 239-252
  • Analytic disks with boundaries in a maximally real submanifold of , Annales de l'institut Fourier, Volume 37, 1987, pp. 1-44
  • Polynomial hulls of sets fibered over the circle , Indiana University Mathematics Journal, Volume 37, 1988, pp. 869-889
  • Extending proper holomorphic mappings of positive codimension , Inventiones Mathematicae, Volume 95, 1989, pp. 31-61
  • Complex tangents of real surfaces in complex surfaces , Duke Math. J., Volume 67, 1992, pp. 353-376
  • with JP Rosay: Approximation of biholomorphic mappings by automorphisms of , Inventiones Mathematicae, Volume 112, 1993, pp. 323-349
  • Proper holomorphic mappings: a survey , in: Several complex Variables, Volume 38, 1993, pp. 297-363 (Proc. Mittag-Leffler-Institut 1987/88)
  • Actions of ( , +) and ( , +) on complex manifolds , Mathematische Zeitschrift, Volume 223, 1996, pp. 123-154
  • Interpolation by holomorphic automorphisms and embeddings in , Journal fo Geometric Analysis, Volume 9, 1999, p. 93
  • with J. Prezelj: Oka's principle for holomorphic submersions with sprays , Arxiv 2001
  • with J. Prezelj: Oka's principle for holomorphic fiber bundles with sprays , Arxiv , 2003
  • The homotopy principle in complex analysis: a survey , Contemporary Math., Volume 332, 2003, pp. 78-199, Arxiv
  • Noncritical holomorphic functions on Stein manifolds , Acta Mathematica, Volume 191, 2003, pp. 143-189, Arxiv
  • with Barbara D. Drnovšek: Holomorphic curves in complex spaces , Duke Math. J., Volume 139, 2007, pp. 203-253, Arxiv
  • Oka manifolds , Compte Rend. Acad. Sci. Paris, Volume 347, 2009, pp. 1017-1020, Arxiv
  • Stein manifolds and holomorphic mappings , Springer 2011, 2017
  • with F. Lárusson: Survey of Oka theory , New York J. Math. A, Volume 17, 2011, pp. 11-38, Arxiv
  • Oka manifolds: From Oka to Stein and back , Ann. Fac. Sci. Toulouse Math., Volume 22, 2013, pp. 747-809, Arxiv

Web links

Individual evidence

  1. Franc Forstnerič in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. Information in his CV in English
  3. Gromov, Oka principle for holomorphic sections of elliptic bundles, J. Am. Math. Soc., Vol. 2, 1989, pp. 851-897
  4. Forstneric, Oka manifolds, CR Math. Acad. Sci. Paris, Volume 347, 2009, pp. 1017-1020
  5. On Oka manifolds: Finnur Lárusson: What is an Oka-Manifold?, Notices AMS, January 2010