Thin triangles and a multiplicative ergodic theorem for Teichm\"uller geometry
Geometric Topology
2007-05-23 v1 Dynamical Systems
Abstract
We show that, in the Teichm\"uller metric, "thin-framed triangles are thin"---that is, under suitable hypotheses, the variation of geodesics obeys a hyperbolic-like inequality. This theorem has applications to the study of random walks on Teichm\"uller space. In particular, an application is worked out for the action of the mapping class group: we show that geodesics track random walks sublinearly.
Cite
@article{arxiv.math/0508046,
title = {Thin triangles and a multiplicative ergodic theorem for Teichm\"uller geometry},
author = {Moon Duchin},
journal= {arXiv preprint arXiv:math/0508046},
year = {2007}
}
Comments
23 pages