2007/08/31 by Franc Forstnerič, Franc Forstneric, Erlend Fornæss Wold +1 · 2 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.AG #math.CV #msc:14H55 #msc:32C22 #msc:32E10 #msc:32H05 #msc:32M17
paper · pdf · doi:10.1016/j.matpur.2008.09.010
published as J. Math. Pures Appl. 91 (2009), no. 1, 100-114 · 24 pages, 2 figures. To appear in J. Math. Pure Appl
arxiv created 2008/10/02 · openalex publication_date 2008/10/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02
One of the oldest open problems in the classical function theory is whether every open Riemann surface admits a proper holomorphic embedding into C2. In this paper we prove the following Theorem: If D is a bordered Riemann surface whose closure admits an injective immersion in C2 that is holomorphic in D, then D admits a proper holomorphic embedding in C2. The most general earlier results are due to J. Globevnik and B. Stensones (Math. Ann. 303 (1995), 579-597) and E. F. Wold (Internat. J. Math. 17 (2006), 963-974). We give an explicit and elementary construction that does not require the Teichmuller space theory, and we also indicate another possible proof using the latter theory.