Some new results on domains in complex space with non-compact automorphism group

Abstract

We provide a new proof of the Wong–Rosay theorem, using the structure of the ring of holomorphic functions. As a byproduct, we provide an analogous theorem for classical bounded symmetric domains. The second main result of this article concerns a new existence theorem for holomorphic peaking functions at a hyperbolic orbit accumulation boundary point. Finally, we give a proof of a version of the Greene–Krantz conjecture using holomorphic vector fields and a strengthened Hopf lemma.