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

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

2010-02-20

arxiv.org/abs/1002.3939v1

Mathematics

Geometric Topology

25 pages, 2 figures

Scientific paper

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.

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