Abstract
Let $\Omega\subset\mathbb C^2$ be a smoothly bounded domain. We prove that if $\partial \Omega$ contains a (small) smooth curve of points of infinity type, then the automorphism group $\Aut(\Omega)$ is compact. This result implies the Greene-Krantz conjecture for a special class of domains. The proof makes no use of scaling techniques.
Citation
Mario Landucci. "The automorphism group of domains with boundary points of infinite type." Illinois J. Math. 48 (3) 875 - 885, Fall 2004. https://doi.org/10.1215/ijm/1258131057
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