Bordered Riemann surfaces in C^2

dc.creatorForstneric, Franc
dc.creatorWold, Erlend Fornaess
dc.date2007-08-21
dc.date2008-10-02
dc.date.accessioned2026-07-07T12:34:39Z
dc.date.available2026-07-07T12:34:39Z
dc.descriptionOne of the oldest open problems in the classical function theory is whether every open Riemann surface admits a proper holomorphic embedding into C^2. In this paper we prove the following Theorem: If D is a bordered Riemann surface whose closure admits an injective immersion in C^2 that is holomorphic in D, then D admits a proper holomorphic embedding in C^2. 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.
dc.description24 pages, 2 figures. To appear in J. Math. Pure Appl
dc.identifierhttps://arxiv.org/abs/0708.2887
dc.identifierhttp://arxiv.org/abs/0708.2887
dc.identifierJ. Math. Pures Appl. 91 (2009), no. 1, 100-114
dc.identifierdoi:10.1016/j.matpur.2008.09.010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217509
dc.subjectComplex Variables
dc.subjectAlgebraic Geometry
dc.subject32C22, 32E10, 32H05, 32M17 (Primary); 14H55 (Secondary)
dc.titleBordered Riemann surfaces in C^2
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