Some properties of $h$-extendible domains in ${\mathbb{C}}^{n+1}$

Abstract

The purpose of this article is twofold. The first aim is to characterize $h$-extendibility of smoothly bounded pseudoconvex domains in ${\mathbb{C}}^{n+1}$ by their noncompact automorphism groups. Our second goal is to show that if the squeezing function tends to $1$ at an $h$-extendible boundary point of a smooth pseudoconvex domain in ${\mathbb{C}}^{n+1}$, then this point must be strongly pseudoconvex.

15 pages