The Weil-Petersson metric and volumes of 3-dimensional hyperbolic convex cores

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dc.creatorBrock, Jeffrey F.
dc.date2001-09-06
dc.date2003-01-23
dc.date.accessioned2026-07-07T04:43:18Z
dc.date.available2026-07-07T04:43:18Z
dc.descriptionWe introduce a coarse combinatorial description of the Weil-Petersson distance d_WP(X,Y) between two finite area hyperbolic Riemann surfaces X and Y. The combinatorics reveal a connection between Riemann surfaces and hyperbolic 3-manifolds conjectured by Thurston: the volume of the convex core of the quasi-Fuchsian manifold Q(X,Y) with X and Y in its boundary is comparable to the Weil-Petersson distance d_WP(X,Y). Applications include a connection of the Weil-Petersson distance with the Hausdorff dimension of the limit set and the lowest eigenvalue of the Laplacian as well as a new finiteness criterion for geometric limits.
dc.description48 pages, 14 figures. Revised final version. To appear, J. Amer. Math. Soc
dc.identifierhttps://arxiv.org/abs/math/0109048
dc.identifierhttp://arxiv.org/abs/math/0109048
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62158
dc.subjectGeometric Topology
dc.subjectDynamical Systems
dc.subject2000 MSC. Primary 30F40; Secondary 30F60, 37F30
dc.titleThe Weil-Petersson metric and volumes of 3-dimensional hyperbolic convex cores
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