Analysis of orbit accumulation points and the Greene-Krantz conjecture

Bingyuan Liu

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arXiv · 1407.5546

Analysis of orbit accumulation points and the Greene-Krantz conjecture

Bingyuan Liu

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Abstract

In $\mathbb{C}^2$, we classify the domains for which $\rm Aut(\Omega)$ is noncompact and describe these domains by their defining functions. This note is based on the technique of the scaling method introduced by Frankel \cite{Fr86} and Kim \cite{Ki90}. 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, $\rm Aut(\Omega)$ contains $\mathbb{R}$, which is an extension of \cite{Fr86}.

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Bingyuan Liu. 2014-07-21. Analysis of orbit accumulation points and the Greene-Krantz conjecture. https://arxiv.org/abs/1407.5546

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