The Hilbert metric on Teichm\"uller space and Earthquake
Geometric Topology
2017-03-09 v1 Complex Variables
Metric Geometry
Abstract
Hamenst\"adt gave a parametrization of the Teichm\"uller space of punctured surfaces such that the image under this parametrization is the interior of a polytope. In this paper, we study the Hilbert metric on the Teichm\"uller space of punctured surfaces based on this parametrization. We prove that every earthquake ray is an almost geodesic under the Hilbert metric.
Keywords
Cite
@article{arxiv.1703.02683,
title = {The Hilbert metric on Teichm\"uller space and Earthquake},
author = {Huiping Pan},
journal= {arXiv preprint arXiv:1703.02683},
year = {2017}
}
Comments
20 pages, 5 figures