Vol. 237, No. 1, 2008

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ISSN: 0030-8730
Lines of minima are uniformly quasigeodesic

Young-Eun Choi, Kasra Rafi and Caroline Series

Vol. 237 (2008), No. 1, 21–44
Abstract

We continue the comparison between lines of minima and Teichmüller geodesics begun in our previous work. For two measured laminations ν+ and ν that fill up a hyperbolizable surface S and for t in (−∞,), let Lt be the unique hyperbolic surface that minimizes the length function etl(ν+) + etl(ν) on Teichmüller space. We prove that the path tLt is a Teichmüller quasigeodesic.

Keywords
lines of minima, Teichmüller space, quasigeodesic
Mathematical Subject Classification 2000
Primary: 30F60
Milestones
Received: 14 June 2007
Revised: 25 February 2008
Accepted: 10 March 2008
Published: 1 September 2008
Authors
Young-Eun Choi
Department of Mathematics and Statistics
3000 Ivyside Park
Altoona, PA 16601
United States
http://math.aa.psu.edu/~choiye/
Kasra Rafi
Department of Mathematics
5734 S. University Avenue
Chicago, IL 60637
United States
http://www.math.uchicago.edu/~rafi/
Caroline Series
Mathematics Institute
University of Warwick
Coventry CV4 7AL
United Kingdom
http://www.warwick.ac.uk/~masbb/