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arXiv · 1401.2841

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

Franc Forstneric·Erlend Fornaess Wold
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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 $<n$.

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Franc Forstneric, Erlend Fornaess Wold. 2014-01-13. Fatou-Bieberbach domains in $\mathbb C^n\setminus\mathbb R^k$. https://doi.org/10.1007/s11512-014-0209-4

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