Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A uniform Sobolev inequality for ancient Ricci flows with bounded Nash
  entropy   This note is a continuation of [CMZ21]. We shall show that an ancient Ricci
flow with uniformly bounded Nash entropy must also have uniformly bounded
$\nu$-functional. Consequently, on such an ancient solution there are uniform
logarithmic Sobolev and Sobolev inequalities. We emphasize that the main
theorem in this paper is true so long as the theory in [Bam20c] is valid, and
in particular, when the underlying manifold is closed.

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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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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: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph