In C 2 , we classify the domains for which Aut(Ω) is noncompact and describe these domains by their defining functions. This note is based on the technique of the scaling method introduced by Frankel [5] and Kim [8]. One feature of this article is that we are able to analyze the defining functions of infinite type boundary. As a corollary, we also prove a result that under some conditions, Aut(Ω) contains R, which is an extension of [5].
In this paper, finite type domains with hyperbolic orbit accumulation points are studied. We prove, in case of C 2 , it has to be a (global) pseudoconvex domain, after an assumption of boundary regularity. Moreover, one of the applications will realize the classification of domains within this class, precisely the domain is biholomorphic to one of the ellipsoids {(z, w) : |z| 2m +|w| 2 < 1, m ∈ Z + }. This application generalizes [4] in which the boundary is assumed to be real analytic for the case of hyperbolic orbit accumulation points.
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