Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the renormalized volume of hyperbolic 3-manifolds   The renormalized volume of hyperbolic manifolds is a quantity motivated by
the AdS/CFT correspondence of string theory and computed via a certain
regularization procedure. The main aim of the present paper is to elucidate its
geometrical meaning. We use another regularization procedure based on surfaces
equidistant to a given convex surface \partial N. The renormalized volume
computed via this procedure is equal to what we call the W-volume of the convex
region N given by the usual volume of N minus the quarter of the integral of
the mean curvature over \partial N. The W-volume satisfies some remarkable
properties. First, this quantity is self-dual in the sense explained in the
paper. Second, it verifies some simple variational formulas analogous to the
classical geometrical Schlafli identities. These variational formulas are
invariant under a certain transformation that replaces the data at \partial N
by those at infinity of M. We use the variational formulas in terms of the data
at infinity to give a simple geometrical proof of results of Takhtajan et al on
the Kahler potential on various moduli spaces.

31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org