Almost-isometry between Teichm\"{u}ller metric and length-spectra metric on moduli space
Geometric Topology
2010-12-10 v1
Abstract
We prove an analogue of Farb-Masur's theorem that the length-spectra metric on moduli space is "almost isometric" to a simple model which is induced by the cone metric over the complex of curves. As an application, we know that the Teichm\"{u}ller metric and the length-spectra metric are "almost isometric" on moduli space, while they are not even quasi-isometric on Teichm\"{u}ller space.
Keywords
Cite
@article{arxiv.1012.1921,
title = {Almost-isometry between Teichm\"{u}ller metric and length-spectra metric on moduli space},
author = {Lixin Liu and Weixu Su},
journal= {arXiv preprint arXiv:1012.1921},
year = {2010}
}