Generalized reinhardt domains
Tóm tắt
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.
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