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.
The automorphism group of domains with boundary points of infinite type / M. LANDUCCI. - In: ILLINOIS JOURNAL OF MATHEMATICS. - ISSN 0019-2082. - STAMPA. - 48,3:(2004), pp. 875-885. [10.1215/ijm/1258131057]
The automorphism group of domains with boundary points of infinite type
LANDUCCI, MARIO
2004
Abstract
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.
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