Domains in Complex Surfaces with a Noncompact Automorphism Group – II

Let X be an arbitrary complex surface and D ⊂ X a domain that has a noncompact 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' ⊂ X is obtained.