Automorphisms and equivalence of bounded Reinhardt domains not containing the origin
type: Item
instance of: scholarly article
title: Automorphisms and equivalence of bounded Reinhardt domains not containing the origin
zbMATH Open document ID: 0646.32003
author: Satoru Shimizu
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1988-01-01T00:00:00Z
review text: The author gives an answer to the equivalence problem for bounded Reinhardt domains, that is, domains in \({\mathbb{C}}^ n\) which are invariant under rotation about the coordinate axes. This problem has already been solved for Reinhardt domains containing the origin, see \textit{T. Sunada}, Math. Ann. 235, 111-128 (1978; Zbl 0357.32001), and for Reinhardt domains containing some points with ith coordinate zero for \(0\leq i\leq k\) and no points with ith coordinate zero for \(k+1\leq i\leq n\) for some k, see \textit{D. Barrett}, Comment. Math. Helv. 59, 550-564 (1984; Zbl 0601.32030). The author also determines the automorphisms of a certain class of bounded Reinhardt domains not containing the origin. His approach is primarily group-theoretic as opposed to the analytic techniques of Barrett and Bedford [\textit{E. Bedford}, Pac. J. Math. 87, 271-281 (1980; Zbl 0449.32024)].
reviewed by: Dennis M. Snow
Mathematics Subject Classification ID: 32A07
Mathematics Subject Classification ID: 32M05
zbMATH DE Number: 4054028
zbMATH Keywords: equivalence
zbMATH Keywords: automorphisms
zbMATH Keywords: bounded Reinhardt domains not containing the origin
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228082
OpenAlex ID: W1985053555
cites work: Holomorphic equivalence and proper mapping of bounded Reinhardt domains not containing the origin
cites work: Holomorphic mapping of products of annuli in \(\mathbb{C}^n\)
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cites work: Q5731354
cites work: Q5628476
cites work: Holomorphic equivalence problem for bounded Reinhardt domains
cites work: Zu den Abbildungen durch analytische Funktionen mehrerer komplexer Veränderlichen. Die Invarianz des Mittelpunktes von Kreiskörpern
DOI: 10.2748/TMJ/1178228082
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description: scientific article; zbMATH DE number 4054028