The Automorphism Group of a Domain with an Exponentially Flat Boundary Point

TL;DR

This paper investigates the automorphism groups of bounded complex domains with exponentially flat boundary points, revealing their typical compactness and providing new examples through their analysis.

Contribution

It introduces new examples of domains with exponentially flat boundary points and analyzes their automorphism groups, highlighting their compactness.

Findings

Automorphism groups are typically compact for such domains.

New examples of domains with exponentially flat boundary points are generated.

The study advances understanding of boundary behavior in complex analysis.

Abstract

We study the automorphisms group action on a bounded domain in $\CC^n$ having a boundary point that is exponentially flat. Such a domain typically has a compact automorphism group. Our results enable us to generate many new examples.