Geometric Properties of Boundary Orbit Accumulation Points

TL;DR

This paper investigates the geometric characteristics of boundary orbit accumulation points in bounded domains in complex space, focusing on their Levi geometric properties under automorphism group actions.

Contribution

It introduces new geometric conditions for boundary orbit accumulation points using Levi geometry, enhancing understanding of automorphism group dynamics.

Findings

Boundary orbit points exhibit specific Levi geometric properties.

Automorphism groups influence boundary geometry in predictable ways.

New criteria for boundary point classification in complex domains.

Abstract

We study the automorphism group action on a bounded domain in $\CC^n$. In particular, we consider boundary orbit accumulation points, and what geometric properties they must have. These properties are formulated in the language of Levi geometry.