Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positivity of the renormalized volume of almost-Fuchsian hyperbolic
  $3$-manifolds   We prove that the renormalized volume of almost-Fuchsian hyperbolic
$3$-manifolds is non-negative, with equality only for Fuchsian manifolds.

31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat