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

TL;DR

This paper characterizes $h$-extendibility of smooth pseudoconvex domains in complex space via their automorphism groups and links the squeezing function approaching 1 to strong pseudoconvexity at boundary points.

Contribution

It provides a new characterization of $h$-extendibility using automorphism groups and relates the squeezing function behavior to boundary pseudoconvexity.

Findings

$h$-extendibility characterized by automorphism groups.

Squeezing function tending to 1 implies boundary strong pseudoconvexity.

Results deepen understanding of boundary geometry in complex analysis.

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.