Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large outlying stable constant mean curvature spheres in initial data
  sets   We give examples of asymptotically flat three-manifolds $(M,g)$ which admit
arbitrarily large constant mean curvature spheres that are far away from the
center of the manifold. This resolves a question raised by G. Huisken and S.-T.
Yau in 1996. On the other hand, we show that such surfaces cannot exist when
$(M,g)$ has nonnegative scalar curvature. This result depends on an intricate
relationship between the scalar curvature of the initial data set and the
isoperimetric ratio of large stable constant mean curvature surfaces.

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The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: stat
18
The categories of this paper are: econ
3
The categories of this paper are: physics
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an