Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite extinction time for the solutions to the Ricci flow on certain
  three-manifolds   Let M be a closed oriented three-manifold, whose prime decomposition contains
no aspherical factors. We show that for any initial riemannian metric on M the
solution to the Ricci flow with surgery, defined in our previous paper
math.DG/0303109, becomes extinct in finite time. The proof uses a version of
the minimal disk argument from 1999 paper by Richard Hamilton, and a
regularization of the curve shortening flow, worked out by Altschuler and
Grayson.

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The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg