The Weil-Petersson metric geometry

Details The Weil-Petersson metric geometry The Weil-Petersson metric geometry

2007-12-31

arxiv.org/abs/0801.0175v1

Mathematics

Differential Geometry

Scientific paper

A summary introduction of the Weil-Petersson metric space geometry is presented. Teichmueller space and its augmentation are described in terms of Fenchel-Nielsen coordinates. Formulas for the gradients and Hessians of geodesic-length functions are presented. Applications are considered. A description of the Weil-Petersson metric in Fenchel-Nielsen coordinates is presented. The Alexandrov tangent cone at points of the augmentation is described. A comparison dictionary is presented between the geometry of the space of flat tori and Teichmueller space with the Weil-Petersson metric.

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