Domains in \(\mathbb{C}^ n\) with a piecewise Levi flat boundary which possess a noncompact automorphism group
type: Item
instance of: scholarly article
title: Domains in \(\mathbb{C}^ n\) with a piecewise Levi flat boundary which possess a noncompact automorphism group
zbMATH Open document ID: 0735.32021
DOI: 10.1007/BF01444637
author: Kang-Tae Kim
published in: Mathematische Annalen
publication date: 1992-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164930
review text: We prove that any bounded convex domain in \(\mathbb{C}^ n\) with a piecewise smooth Levi flat boundary which possesses a noncompact automorphism group is reducible in the sense that it is biholomorphic to a product domain. This, in particular, characterizes the bi-disk in \(\mathbb{C}^ 2\) by its automorphism group.
Mathematics Subject Classification ID: 32M05
zbMATH DE Number: 4215923
zbMATH Keywords: bounded convex domain
zbMATH Keywords: Levi flat boundary
zbMATH Keywords: noncompact automorphism group
zbMATH Keywords: biholomorphic to a product domain
MaRDI profile type: Publication
cites work: Complex geometry of convex domains that cover varieties
cites work: Invariants of Bergman geometry and the automorphism groups of domains in \({\mathbb{C}^n}\)
cites work: Complete Localization of Domains with Noncompact Automorphism Groups
cites work: Q5608188
cites work: On the structure of a bounded domain with a special boundary point
cites work: Q3924489
cites work: Q3976251
cites work: Homogeneous domains with piecewise-smooth boundaries
cites work: Sur une caractérisation de la boule parmi les domaines de \(\mathbb{C}^n\) par son groupe d'automorphismes
cites work: Characterization of the unit ball in \(\mathbb{C}^n\) by its automorphism group
cites work: Normal families of holomorphic mappings
OpenAlex ID: W2065197253
description: scientific article; zbMATH DE number 4215923