Proper holomorphic embeddings of Riemann surfaces with arbitrary topology into $\mathbb{C}^2$

Details Proper holomorphic embeddings of Riemann surfaces with arbitrary topology into $\mathbb{C}^2$ Proper holomorphic embeddings of Riemann surfaces with arbitrary topology into $\mathbb{C}^2$

2011-04-11

arxiv.org/abs/1104.1893v1

Mathematics

Complex Variables

8 pages

Scientific paper

We prove that given an open Riemann surface $N,$ there exists an open domain
$M\subset N$ homeomorphic to $N$ which properly holomorphically embeds in
$\mathbb{C}^2.$ Furthermore, $M$ can be chosen with hyperbolic conformal type.
In particular, any open orientable surface admits a complex structure properly
holomorphically embedding into $\mathbb{C}^2.$

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