The Weil-Petersson geometry of the five-times punctured sphere
arXiv:math/0501552
Abstract
We give a new proof that the completion of the Weil-Petersson metric on Teichmüller 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.
11 pages. Revised version, to appear in "Spaces of Kleinian Groups", LMS Lecture Notes, Eds. Y.Minsky, M.Sakuma, C.Series