Analysis of Orbit Accumulation Points and The Greene–Krantz Conjecture

Abstract

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].