Length of a curve is quasi-convex along a Teichmuller geodesic

2010/02/20 by Anna Lenzhen, Lenzhen, Anna, Kasra Rafi +1
Mathematics · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.1002.3939

Abstract

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

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