Open Access
June 2011 Length of a Curve is Quasi-Convex Along a Teichmüller Geodesic
Anna Lenzhen, Kasra Rafi
J. Differential Geom. 88(2): 267-295 (June 2011). DOI: 10.4310/jdg/1320067648


We show that for every simple closed curve 𝛼, the extremal length and the hyperbolic length of 𝛼 are quasi-convex functions along any Teichmüller geodesic. As a corollary, we conclude that, in Teichmüller space equipped with the Teichmüller metric, balls are quasi-convex.


Download Citation

Anna Lenzhen. Kasra Rafi. "Length of a Curve is Quasi-Convex Along a Teichmüller Geodesic." J. Differential Geom. 88 (2) 267 - 295, June 2011.


Published: June 2011
First available in Project Euclid: 31 October 2011

zbMATH: 1243.30089
MathSciNet: MR2838267
Digital Object Identifier: 10.4310/jdg/1320067648

Rights: Copyright © 2011 Lehigh University

Vol.88 • No. 2 • June 2011
Back to Top