Some properties of h-extendible domains in [formula omitted

Abstract

The purpose of this article is twofold. The first aim is to characterize h-extendibility of smoothly bounded pseudoconvex domains in Cn+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 Cn+1, then this point must be strongly pseudoconvex.