Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differential Harnack Estimates for Parabolic Equations   Let $(M,g(t))$ be a solution to the Ricci flow on a closed Riemannian
manifold. In this paper, we prove differential Harnack inequalities for
positive solutions of nonlinear parabolic equations of the type $$\ppt f=\Delta
f-f \ln f +Rf.$$ We also comment on an earlier result of the first author on
positive solutions of the conjugate heat equation under the Ricci flow.

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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
1
The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org