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arXiv · 0708.2887

Bordered Riemann surfaces in C^2

Franc Forstneric·Erlend Fornaess Wold
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Abstract

One 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.

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Franc Forstneric, Erlend Fornaess Wold. 2008-10-02. Bordered Riemann surfaces in C^2. https://doi.org/10.1016/j.matpur.2008.09.010

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