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arXiv · 1307.8359

Geometric properties of semitube domains

Łukasz Kosiński·Tomasz Warszawski·Włodzimierz Zwonek
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Abstract

In the paper we study the geometry of semitube domains in $\mathbb C^2$. In particular, we extend the result of Burgu\'es and Dwilewicz for semitube domains dropping out the smoothness assumption. We also prove various properties of non-smooth pseudoconvex semitube domains obtaining among others a relation between pseudoconvexity of a semitube domain and the number of connected components of its vertical slices. Finally, we present an example showing that there is a non-convex domain in $\mathbb C^n$ such that its image under arbitrary isometry is pseudoconvex.

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Łukasz Kosiński, Tomasz Warszawski, Włodzimierz Zwonek. 2013-07-31. Geometric properties of semitube domains. https://doi.org/10.1515/advgeom-2015-0010

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