Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric characterizations of asymptotically hyperbolic Riemannian
  3-manifolds by the existence of a suitable CMC-foliation   In 1996, Huisken-Yau proved that every three-dimensional Riemannian manifold
can be uniquely foliated near infinity by stable closed surfaces of constant
mean curvature (CMC) if it is asymptotically equal to the (spatial)
Schwarzschild solution. Using their method, Rigger proved the same theorem for
Riemannian manifolds being asymptotically equal to the (spatial)
(Schwarzschild-)Anti-de Sitter solution. This was generalized to asymptotically
hyperbolic manifolds by Neves-Tian, Chodosh, and the author at a later stage.
In this work, we prove the reverse implication as the author already did in the
Euclidean setting, i.e. any three-dimensional Riemannian manifold is
asymptotically hyperbolic if it (and only if) possesses a CMC-cover satisfying
certain geometric curvature estimates, a uniqueness property, and each surface
has controlled instability. As toy application of these geometric
characterizations of asymptotically Euclidean and hyperbolic manifolds, we
present a method for replacing an asymptotically hyperbolic by an
asymptotically Euclidean end and apply this method to prove that the Hawking
mass of the CMC-surfaces is bounded by their limit being the total mass of the
asymptotically hyperbolic manifold, where equality holds only for the t=0-slice
of the (Schwarzschild-)Anti-de Sitter spacetime.

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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph