Holomorphic families of Fatou-Bieberbach domains and applications to Oka manifolds

Abstract

We construct holomorphically varying families of Fatou-Bieberbach domains with given centres in the complement of any compact polynomially convex subset $K$ of ${\mathbb{C}}^n$ for $n>1$. This provides a simple proof of the recent result of Yuta Kusakabe to the effect that the complement ${\mathbb{C}}^n\setminus K$ of any polynomially convex subset $K$ of ${\mathbb{C}}^n$ is an Oka manifold. The analogous result is obtained with ${\mathbb{C}}^n$ replaced by any Stein manifold with the density property.

A few minor corrections were made. To appear in Math. Res. Lett

References in corpus (1)

• Oka properties of complements of holomorphically convex sets

Cited by in corpus (6)

• Recent developments on Oka manifolds
• The first thirty years of Andersen-Lempert theory
• Oka domains in Euclidean spaces
• Euclidean domains in complex manifolds
• Oka tubes in holomorphic line bundles
• Oka-1 manifolds