Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropy Functionals, Sobolev Inequalities and kappa-Noncollapsing
  Estimates along the Ricci Flow   In this survey we review Hamilton's entropy and Perelman's entropy, and
provide motivations for these concepts. Then we review recent results on the
logarithmic Sobolev inequality, the Sobolev inequalities and
kappa-noncollapsing estimates along the Ricci flow, including the Ricci flow
with surgeries.

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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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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: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci