The union problem for domains with partial pseudoconvex boundaries

Abstract

We show that a smooth bounded domain in ${\mathbb{C}}^n$ admitting partial pseudoconvex exhaustion remains partial pseudoconvex. The main ingredient of the proof is based on a new characterization of hyper-$q$-convex domains. Furthermore, we get several convex analogies.

Some remarks added in the the Introduction, and references are updated