Semi-continuity of Automorphism Groups of Strongly Pseudoconvex Domains: the low differentiability case

TL;DR

This paper investigates how automorphism groups of strongly pseudoconvex domains behave under perturbations, especially focusing on cases with minimal boundary smoothness and introducing a new approach for low differentiability scenarios.

Contribution

It presents a novel methodology for analyzing the semicontinuity of automorphism groups in domains with low boundary smoothness, expanding understanding in less regular settings.

Findings

Established semicontinuity results for automorphism groups with minimal boundary smoothness

Developed a new approach tailored to low differentiability cases

Extended classical results to broader classes of domains

Abstract

We study the semicontinuity of automorphism groups for perturbations of domains in complex space or in complex manifolds. We provide a new approach to the study of such results for domains having minimal boundary smoothness. The emphasis in this study is on the low differentiability assumption and the new methodology developed accordingly.