%0 Journal Article
%T The Weil-Petersson metric and volumes of 3-dimensional hyperbolic convex cores
%A Jeffrey F. Brock
%J Mathematics
%D 2001
%I arXiv
%X We 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.
%U http://arxiv.org/abs/math/0109048v2