Fatou-Bieberbach domains in ${\mathbb{C}}^n\setminus {\mathbb{R}}^k$

Abstract

We construct Fatou-Bieberbach domains in ${\mathbb{C}}^n$ for $n>1$ which contain a given compact set $K$ and at the same time avoid a totally real affine subspace $L$ of dimension $<n$, provided that $K\cup L$ is polynomially convex. By using this result, we show that the domain ${\mathbb{C}}^n\setminus {\mathbb{R}}^k$ for $1\le k<n$ enjoys the Oka property with approximation for maps from any Stein manifold of dimension $<n$.

To appear in Ark. Mat

References in corpus (2)

• Oka properties of ball complements
• Holomorphic flexibility properties of compact complex surfaces

Cited by in corpus (1)

• The first thirty years of Andersen-Lempert theory