The Weil-Petersson geometry of the five-times punctured sphere
Abstract
Description
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
11 pages. Revised version, to appear in "Spaces of Kleinian Groups", LMS Lecture Notes, Eds. Y.Minsky, M.Sakuma, C.Series