A soft Oka principle for proper holomorphic embeddings of open Riemann surfaces into $({\mathbb{C}}^{\ast }{)}^2$

Abstract

Let $X$ be an open Riemann surface. We prove an Oka property on the approximation and interpolation of continuous maps $X\to ({\mathbb{C}}^{\ast }{)}^2$ by proper holomorphic embeddings, provided that we permit a smooth deformation of the complex structure on $X$ outside a certain set. This generalises and strengthens a recent result of Alarcon and Lopez. We also give a Forstneric-Wold theorem for proper holomorphic embeddings (with respect to the given complex structure) of certain open Riemann surfaces into $({\mathbb{C}}^{\ast }{)}^2$.

References in corpus (1)

• Bordered Riemann surfaces in C^2