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

Javier Aramayona
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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.

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Javier Aramayona. 2005-04-12. The Weil-Petersson geometry of the five-times punctured sphere. https://arxiv.org/abs/math/0501552

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