Analytic polyhedra in C-2 with a non-compact automorphism group

Abstract

We show that a bounded domain in C-2 with an automorphism. orbit accumulating at a point in a certain non-trivial variety contained in the boundary is biholomorphic to a product of the disc and the variety. This in particular gives rise to an optimal characterization of bounded normal analytic polyhedra in C-2 admitting a noncompact automorphism group.