Geometric properties of semitube domains

Abstract

Abstract. In the paper we study the geometry of semitube domains in 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 components of its vertical slices.Finally, we present an example showing that there is a non-convex domain in C n such that its image under arbitrary isometry is pseudoconvex.

Complex geodesics in convex tube domains II

“…It is a generalization of semitube domains (sets) in C 2 introduced in [BD12] and studied in [KWZ15]. Note that any tube domain (set) is a semitube one.…”