Bordered Riemann surfaces in C2

By F. Forstnerič, E. F. Wold. 2007

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Abstract We prove that the interior of any compact complex curve with smooth boundary in C 2 admits a proper holomorphic embedding into C 2 . In particular, if D is a bordered Riemann surface whose closure admits a holomorphic embedding into C 2 , then D admits a proper holomorphic embedding into C 2 .

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1aa8113968b1549e76020807bb10905ce413af3d

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Holomorphic Approximation: The Legacy of Weierstrass, Runge, Oka–Weil, and Mergelyan (2018, background): “y in complexanalysis (for instance, in constructionsof closed complex curves in complex manifolds, see [44], or in constructions of proper holomorphic embeddings of open Riemann surfaces into C2, see [66, 67] and [68, Chap. 9]), but also in related areas such as the theory of minimal surfaces in Euc”
On the present state of the Andersen-Lempert theory (2010, background): “Some additional technical development concerning the Forster conjecture can be found in [40] and [68].”
Survey of Oka theory (2010, result): “For recent results in this direction, see [26, 52].”