Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Insufficient convergence of inverse mean curvature flow on
  asymptotically hyperbolic manifolds   We construct a solution to inverse mean curvature flow on an asymptotically
hyperbolic 3-manifold which does not have the convergence properties needed in
order to prove a Penrose--type inequality. This contrasts sharply with the
asymptotically flat case. The main idea consists in combining inverse mean
curvature flow with work done by Shi--Tam regarding boundary behavior of
compact manifolds. Assuming the Penrose inequality holds, we also derive a
nontrivial inequality for functions on $S^2$.

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The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
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
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc