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Oka properties of ball complements |
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| Authors: | Franc Forstnerič Tyson Ritter |
| Affiliation: | 1. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000?, Ljubljana, Slovenia 2. Institute of Mathematics, Physics, and Mechanics, Jadranska 19, 1000?, Ljubljana, Slovenia 3. School of Mathematical Sciences, University of Adelaide, Adelaide, SA, 5005, Australia 4. Matematisk Institutt, Universitetet i Oslo, Postboks 1053 Blindern, 0316?, Oslo, Norway |
| 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 $Lsubset mathbb {C}^n$ satisfy the basic Oka property with approximation and interpolation. If $L$ is polynomially convex then the same holds when $2dim X le n$ . We also construct proper holomorphic maps, immersions and embeddings $Xrightarrow mathbb {C}^n$ with additional control of the range, thereby extending classical results of Remmert, Bishop and Narasimhan. |
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