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arXiv · 1303.2239

Oka properties of ball complements

Franc Forstneric·Tyson Ritter
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Abstract

Let $n>1$ be an integer. We prove that holomorphic maps from Stein manifolds $X$ of dimension $<n$ to the complement $\mathbb{C}^n\setminus L$ of a compact convex set $L\subset\mathbb{C}^n$ satisfy the basic Oka property with approximation and interpolation. If $L$ is polynomially convex then the same holds when $2\dim X < n$. We also construct proper holomorphic maps, immersions and embeddings $X\to\mathbb{C}^n$ with additional control of the range, thereby extending classical results of Remmert, Bishop and Narasimhan.

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Franc Forstneric, Tyson Ritter. 2017-03-29. Oka properties of ball complements. https://doi.org/10.1007/s00209-013-1258-2

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