Volume 3, issue 1 (2003)

Download this article
For printing
Recent Issues

Volume 19
Issue 7, 3217–3753
Issue 6, 2677–3215
Issue 5, 2151–2676
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

Author Index
The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
To Appear
 
Other MSP Journals
Limit points of lines of minima in Thurston's boundary of Teichmüller space

Raquel Diaz and Caroline Series

Algebraic & Geometric Topology 3 (2003) 207–234

arXiv: math.GT/0303108

Abstract

Given two measured laminations μ and ν in a hyperbolic surface which fill up the surface, Kerckhoff [Lines of Minima in Teichmueller space, Duke Math J. 65 (1992) 187–213] defines an associated line of minima along which convex combinations of the length functions of μ and ν are minimised. This is a line in Teichmüller space which can be thought as analogous to the geodesic in hyperbolic space determined by two points at infinity. We show that when μ is uniquely ergodic, this line converges to the projective lamination [μ], but that when μ is rational, the line converges not to [μ], but rather to the barycentre of the support of μ. Similar results on the behaviour of Teichmüller geodesics have been proved by Masur [Two boundaries of Teichmueller space, Duke Math. J. 49 (1982) 183–190].

Keywords
Teichmüller space, Thurston boundary, measured geodesic lamination, Kerckhoff line of minima
Mathematical Subject Classification 2000
Primary: 20H10
Secondary: 32G15
References
Forward citations
Publication
Received: 17 January 2003
Accepted: 3 February 2003
Published: 26 February 2003
Authors
Raquel Diaz
Deparmento Geometría y Topología
Fac. CC. Matemáticas
Universidad Complutense
28040 Madrid
Spain
Caroline Series
Mathematics Institute
University of Warwick
Coventry CV4 7AL
UK