A characterization of domains in $\mathbf C^2$ with noncompact automorphism group

TL;DR

This paper characterizes bounded domains in complex two-space with noncompact automorphism groups, identifying model domains under specific boundary smoothness and type conditions.

Contribution

It provides a detailed description of such domains when at least one orbit accumulates at a boundary point with smooth, real analytic, finite type boundary.

Findings

Identification of model domains under boundary smoothness conditions

Conditions for noncompact automorphism groups in $ extbf{C}^2$ domains

Characterization of boundary points with finite type for automorphism groups

Abstract

Let $D$ be a bounded domain in $\mathbf C^2$ with a non-compact group of holomorphic automorphisms. Model domains for $D$ are obtained under the hypothesis that at least one orbit accumulates at a boundary point near which the boundary is smooth, real analytic and of finite type.