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

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 ${\mathbb{C}}^2.$

8 pages

References in corpus (1)

• Bordered Riemann surfaces in C^2

Cited by in corpus (1)

• Every bordered Riemann surface is a complete proper curve in a ball