Stably-interior points and the Semicontinuity of the Automorphism group

TL;DR

This paper proves the semicontinuity of automorphism groups for certain complex domains, introducing a new proof method that simplifies earlier results in the field of complex analysis.

Contribution

It presents a novel, simplified proof of semicontinuity of automorphism groups for two-dimensional pseudoconvex domains with smooth boundaries.

Findings

Semicontinuity of automorphism groups established for specified domains.

New proof method simplifies previous complex proofs.

Results extend understanding of automorphism group behavior in complex analysis.

Abstract

The first result is the semicontinuity of automorphism groups for the collection of complex two-dimensional bounded pseudoconvex domains with smooth boundary of finite D'Angelo type. The method of proof is new so that it simplifies the previous proof of earlier semicontinuity theorems on bounded strongly pseudoconvex daomains by Greene and Krantz in the early 1980s.