The Weil-Petersson metric geometry
arXiv:0801.0175
Abstract
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.
References in corpus (6)
- Geometry of the Weil-Petersson completion of Teichmüller space
- Mirzakhani's recursion relations, Virasoro constraints and the KdV hierarchy
- Behavior of geodesic-length functions on Teichmueller space
- Triangulated Riemann surfaces with boundary and the Weil-Petersson Poisson structure
- Average curvatures of Weil-Petersson geodesics in Teichmuller space
- Integration on moduli spaces of stable curves through localization
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- Recent Development on the Geometry of the Teichmuller and Moduli Spaces of Riemann Surfaces and Polarized Calabi-Yau Manifolds
- On a Canonical Quantization of 3D Anti de Sitter Pure Gravity
- Two-parametric hyperbolic octagons and reduced Teichmueller space in genus two
- Grafting hyperbolic metrics and Eisenstein series
- Relativistic Kinematics of Two-Parametric Riemann Surface in Genus Two