Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note on Existence and Non-existence of Minimal Surfaces in Some
  Asymptotically Flat 3-manifolds   Motivated by problems on apparent horizons in general relativity, we prove
the following theorem on minimal surfaces: Let $g$ be a metric on the
three-sphere $S^3$ satisfying $Ric(g) \geq 2 g$. If the volume of $(S^3, g)$ is
no less than one half of the volume of the standard unit sphere, then there are
no closed minimal surfaces in the asymptotically flat manifold $(S^3 \setminus
\{P \}, G^4 g)$. Here $G$ is the Green's function of the conformal Laplacian of
$(S^3, g)$ at an arbitrary point $P$. We also give an example of $(S^3, g)$
with $Ric(g) > 0$ where $(S^3 \setminus \{P \}, G^4 g)$ does have closed
minimal surfaces.

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The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
16
The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an