Volume 11, issue 3 (2007)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 7, 3233–3749
Issue 6, 2701–3231
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Triangle inequalities in path metric spaces

Michael Kapovich

Geometry & Topology 11 (2007) 1653–1680

arXiv: math.MG/0611118

Abstract

We study side-lengths of triangles in path metric spaces. We prove that unless such a space X is bounded, or quasi-isometric to + or to , every triple of real numbers satisfying the strict triangle inequalities, is realized by the side-lengths of a triangle in X. We construct an example of a complete path metric space quasi-isometric to 2 for which every degenerate triangle has one side which is shorter than a certain uniform constant.

Keywords
path metric spaces, triangles
Mathematical Subject Classification 2000
Primary: 51K05
References
Forward citations
Publication
Received: 6 December 2006
Accepted: 30 July 2007
Published: 2 August 2007
Proposed: Walter Neumann
Seconded: Yasha Eliashberg, Martin Bridson
Authors
Michael Kapovich
Department of Mathematics
University of California, Davis
Davis CA 95616
USA
http://www.math.ucdavis.edu/~kapovich/