%0 Journal Article
%T Length of a curve is quasi-convex along a Teichmuller geodesic
%A Anna Lenzhen
%A Kasra Rafi
%J Mathematics
%D 2010
%I arXiv
%X We show that for every simple closed curve \alpha, the extremal length and the hyperbolic length of \alpha are 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.
%U http://arxiv.org/abs/1002.3939v1