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October 2015 Fatou–Bieberbach domains in $\mathbb{C}^{n}\setminus\mathbb{R}^{k}$
Franc Forstnerič, Erlend F. Wold
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Ark. Mat. 53(2): 259-270 (October 2015). DOI: 10.1007/s11512-014-0209-4

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 KL 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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Franc Forstnerič. Erlend F. Wold. "Fatou–Bieberbach domains in $\mathbb{C}^{n}\setminus\mathbb{R}^{k}$." Ark. Mat. 53 (2) 259 - 270, October 2015. https://doi.org/10.1007/s11512-014-0209-4

Information

Received: 23 January 2014; Published: October 2015
First available in Project Euclid: 30 January 2017

zbMATH: 1333.32015
MathSciNet: MR3391171
Digital Object Identifier: 10.1007/s11512-014-0209-4

Rights: 2015 © Institut Mittag-Leffler

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Vol.53 • No. 2 • October 2015
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