Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heat flow on Alexandrov spaces   We prove that on compact Alexandrov spaces with curvature bounded below the
gradient flow of the Dirichlet energy in the $L^2$-space produces the same
evolution as the gradient flow of the relative entropy in the $L^2$-Wasserstein
space. This means that the heat flow is well defined by either one of the two
gradient flows. Combining properties of these flows, we are able to deduce the
Lipschitz continuity of the heat kernel as well as Bakry-\'Emery gradient
estimates and the $\Gamma_2$-condition. Our identification is established by
purely metric means, unlike preceding results relying on PDE techniques. Our
approach generalizes to the case of heat flow with drift.

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The categories of this paper are: astro-ph
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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: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: physics