On the proper conjugation of Kleinian groups
type: Item
instance of: scholarly article
title: On the proper conjugation of Kleinian groups
zbMATH Open document ID: 0836.30028
DOI: 10.1007/BF01267639
author: Qing Zhou
author: Shicheng Wang
published in: Geometriae Dedicata
publication date: 1996-11-13T00:00:00Z
review text: In the paper under review the authors studies geometrically finite Kleinian groups acting isometrically on the hyperbolic space \(\mathbb{H}^n\). The main result of the paper is the following: Theorem. Suppose \(K \in Iso \mathbb{H}^n\) is a geometrically finite nonelementary Kleinian group or an elementary Kleinian group with two fixed points at infinity, and \(g \in Iso \mathbb{H}^n\) is a Möbius transformation. Then \(gKg^{-1} \subset K\) implies that \(gKg^{-1} = K\). Reviewer's remark. The proof of the theorem stated for the whole isometry group \(Iso \mathbb{H}^n\) of the hyperbolic space \(H^n\), is given only for its orientation preserving part \(Iso_+ \mathbb{H}^n\).
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 57S25
zbMATH DE Number: 806252
zbMATH Keywords: Kleinian groups
reviewed by: Leonid Potyagailo
MaRDI profile type: Publication
cites work: Q4692972
cites work: Q3310101
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cites work: On a problem of Heinz Hopf
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cites work: The discrete elementary groups
description: scientific article; zbMATH DE number 806252