Rigid characterizations of pseudoconvex domains

Abstract

We prove that an open set $D$ in $\C^n$ is pseudoconvex if and only if for any $z\in D$ the largest balanced domain centered at $z$ and contained in $D$ is pseudoconvex, and consider analogues of that characterization in the linearly convex case.

v2: Proposition 14 is improved; v3: Example 15 and the proof of Proposition 14 are changed