Discreteness and convergence of Möbius groups
type: Item
instance of: scholarly article
title: Discreteness and convergence of Möbius groups
zbMATH Open document ID: 1053.30038
DOI: 10.1023/B:GEOM.0000023036.55318.40
author: Min Chen
published in: Geometriae Dedicata
publication date: 2004-08-06T00:00:00Z
review text: In this paper, the author shows that a fixed nontrivial Möbius transformation can be used as a test map to test the discreteness of a nonelementary Möbius group. Following Jorgensen's well-known result about the discreteness of a group of Möbius transformations, the author proves two discreteness theorems. The first of these two results says that if for every element g of an n-dimensional subgroup \(G\) of I\(som(Hn)\), the group \(<g,h>\) is discrete , then \(G\) is discrete. The second discreteness theorem states some conditions for the discreteness of G. Also two convergence theorems are given at the end.
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 2081984
zbMATH Keywords: Möbius groups
zbMATH Keywords: algebraic convergence
zbMATH Keywords: discreteness
reviewed by: Ismail Naci Cangül
MaRDI profile type: Publication
full work available at URL: b:geom.0000023036.55318.40
OpenAlex ID: W1985420224
description: scientific article; zbMATH DE number 2081984