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arXiv · 1104.1893

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

Antonio Alarcon·Francisco J. Lopez
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Abstract

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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Antonio Alarcon, Francisco J. Lopez. 2011-04-11. Proper holomorphic embeddings of Riemann surfaces with arbitrary topology into $\mathbb{C}^2$. https://arxiv.org/abs/1104.1893

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