Statistical hyperbolicity in Teichmüller space

Details Statistical hyperbolicity in Teichmüller space Statistical hyperbolicity in Teichmüller space

2011-08-27

arxiv.org/abs/1108.5416v2

Mathematics

Geometric Topology

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Scientific paper

In this paper we explore the idea that Teichm\"uller space with the
Teichm\"uller metric is hyperbolic "on average." We consider several different
measures on Teichm\"uller space and show that with respect to each one, the
average distance between points in a ball of radius r is asymptotic to 2r,
which is as large as possible.

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