Generalized reinhardt domains

Abstract

In this paper we investigate a class of Lie group actions on\(\mathbb{C}^N \), the so-calledpolar actions, that naturally generalize the standard\(\mathbb{T}^N \) actions. For a domain invariant under such an action (i.e., a generalized Reinhardt domain) we characterize the invariant plurisubharmonic functions and determine the envelope of holomorphy in geometric terms. For a generalized Reinhardt domain containing the origin of\(\mathbb{C}^N \) we also compute its automorphism group.