Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Weil-Petersson metric and volumes of 3-dimensional hyperbolic convex
  cores   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.

17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn