The Weil-Petersson geometry of the five-times punctured sphere
Differential Geometry
2007-05-23 v2
Abstract
We give a new proof that the completion of the Weil-Petersson metric on Teichm\"uller space is Gromov-hyperbolic if the surface is a five-times punctured sphere or a twice-punctured torus. Our methods make use of the synthetic geometry of the Weil-Petersson metric.
Keywords
Cite
@article{arxiv.math/0501552,
title = {The Weil-Petersson geometry of the five-times punctured sphere},
author = {Javier Aramayona},
journal= {arXiv preprint arXiv:math/0501552},
year = {2007}
}
Comments
11 pages. Revised version, to appear in "Spaces of Kleinian Groups", LMS Lecture Notes, Eds. Y.Minsky, M.Sakuma, C.Series