The Weil-Petersson metric geometry
By S. Wolpert. 2007
48 citations recorded by the source corpus.
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.
Subfields: Mechanical Engineering
View Paper: https://www.semanticscholar.org/paper/e24407f801b934c366b1b4436823762fedeab9a0
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In Mechanical Engineering
Citations in the corpus
- The renormalized volume and the volume of the convex core of quasifuchsian manifolds (2011, background): “This kind of statement is presumably most interesting close to the boundary of TS for the Weil–Petersson metric, where the sectional curvature tends to be close to 0 in many directions; see [25, 24].”
- Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus (2010, unknown): “For more details, see [M2], [Bu], and [W3].”