Domains in complex surfaces with a non compact automorphism group - II

TL;DR

This paper characterizes complex surface domains with non compact automorphism groups that have smooth real analytic boundary points and are contained in complete hyperbolic domains, advancing understanding of their geometric structure.

Contribution

It provides a new characterization of such domains with boundary orbit accumulation points and their relation to complete hyperbolic domains in complex surfaces.

Findings

Domains with non compact automorphism groups can have smooth real analytic boundary points.

Such domains are contained in complete hyperbolic domains within complex surfaces.

The paper offers a classification of these domains based on boundary and automorphism properties.

Abstract

Let $X$ be an arbitrary complex surface and $D \subset X$ a domain that has a non compact group of holomorphic automorphisms. A characterization of those domains $D$ that admit a smooth real analytic, finite type boundary orbit accumulation point and whose closures are contained in a complete hyperbolic domain $D'\subset X$ is obtained.