Bounded combinatorics and the Lipschitz metric on Teichm\"uller space
Geometric Topology
2011-09-15 v2
Abstract
Considering the Teichm\"uller space of a surface equipped with Thurston's Lipschitz metric, we study geodesic segments whose endpoints have bounded combinatorics. We show that these geodesics are cobounded, and that the closest-point projection to these geodesics is strongly contracting. Consequently, these geodesics are stable. Our main tool is to show that one can get a good estimate for the Lipschitz distance by considering the length ratio of finitely many curves.
Cite
@article{arxiv.1011.6078,
title = {Bounded combinatorics and the Lipschitz metric on Teichm\"uller space},
author = {Anna Lenzhen and Kasra Rafi and Jing Tao},
journal= {arXiv preprint arXiv:1011.6078},
year = {2011}
}
Comments
20 pages, 5 figures; Revised version incorporated referee's comments: expanded the introduction and background, clarified some proofs, and corrected typos