Geometric properties of semitube domains

Abstract

In the paper we study the geometry of semitube domains in ${\mathbb{C}}^2$. In particular, we extend the result of Burgués 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.

6 pages