The Weil-Petersson geometry of the five-times punctured sphere

Details The Weil-Petersson geometry of the five-times punctured sphere The Weil-Petersson geometry of the five-times punctured sphere

2005-01-31

arxiv.org/abs/math/0501552v2

Mathematics

Differential Geometry

11 pages. Revised version, to appear in "Spaces of Kleinian Groups", LMS Lecture Notes, Eds. Y.Minsky, M.Sakuma, C.Series

Scientific paper

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.

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