Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An isoperimetric constant associated to horizons in $S^3$ blown-up at
  two points   Let $g$ be a metric on $S^3$ with positive Yamabe constant. When blowing up
$g$ at two points, a scalar flat manifold with two asymptotically flat ends is
produced and this manifold will have compact minimal surfaces. We introduce the
$\Th$-invariant for $g$ which is an isoperimetric constant for the cylindrical
domain inside the outermost minimal surface of the blown-up metric. Further we
find relations between $\Th$ and the Yamabe constant and the existence of
horizons in the blown-up metric on $\mR^3$.

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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin