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

Franc Forstnerič Faculty of Mathematics and Physics, University of Ljubljana Erlend F. Wold Department of Mathematics, University of Oslo

Functional Analysis mathscidoc:1701.12029

Arkiv for Matematik, 53, (2), 259-270, 2014.1
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$K$∪$L$is polynomially convex. By using this result, we show that the domain $\mathbb{C}^{n}\setminus\mathbb{R}^{k}$ for 1≤$k$<$n$enjoys the basic Oka property with approximation for maps from any Stein manifold of dimension <$n$.
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@inproceedings{franc2014fatou–bieberbach,
  title={Fatou–Bieberbach domains in $\mathbb{C}^{n}\setminus\mathbb{R}^{k}$ },
  author={Franc Forstnerič, and Erlend F. Wold},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203640652974084},
  booktitle={Arkiv for Matematik},
  volume={53},
  number={2},
  pages={259-270},
  year={2014},
}
Franc Forstnerič, and Erlend F. Wold. Fatou–Bieberbach domains in $\mathbb{C}^{n}\setminus\mathbb{R}^{k}$ . 2014. Vol. 53. In Arkiv for Matematik. pp.259-270. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203640652974084.
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