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

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 $D^{\prime }\subset X$ is obtained.