A geometric approach to Jørgensen's inequality
type: Item
instance of: scholarly article
title: A geometric approach to Jørgensen's inequality
zbMATH Open document ID: 0722.30033
DOI: 10.1016/0001-8708(91)90055-C
author: Jane Gilman
published in: Advances in Mathematics
publication date: 1991-01-01T00:00:00Z
review text: Let \(<A,B>\) be a non-elementary purely hyperbolic subgroup of PSL(2,\({\mathbb{R}})\) generated by A and B. It is shown that \(| tr[A,B]- 2| >16\) if the asees of A and B are disjoint and \(| tr[A,B]- 2| >4\) if the asees of A and B intersect and these inequalities are sharp. This result is a trivial consequence and reformulation of a result in [\textit{G. Rosenberger}, Math. Ann. 199, 213-227 (1972; Zbl 0244.20057)] or in [\textit{N. Purzitsky}, Math. Z. 126, 209-223 (1972; Zbl 0232.20104)].
reviewed by: Gerhard Rosenberger
Mathematics Subject Classification ID: 30F35
Mathematics Subject Classification ID: 20H10
zbMATH DE Number: 4190114
zbMATH Keywords: Möbius transformations
zbMATH Keywords: hyperbolic groups
MaRDI profile type: Publication
cites work: Q3770791
cites work: Inequalities in Discrete Subgroups of PSL(2, R)
cites work: A geometric approach to the hyperbolic Jørgensen inequality
cites work: On Discrete Groups of Mobius Transformations
cites work: Two generator discrete free products
cites work: All generating pairs of all two-generator Fuchsian groups
description: scientific article; zbMATH DE number 4190114