Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Properties of Isoperimetric, Functional and Transport-Entropy
  Inequalities Via Concentration   Various properties of isoperimetric, functional, Transport-Entropy and
concentration inequalities are studied on a Riemannian manifold equipped with a
measure, whose generalized Ricci curvature is bounded from below. First,
stability of these inequalities with respect to perturbation of the measure is
obtained. The extent of the perturbation is measured using several different
distances between perturbed and original measure, such as a one-sided
$L^\infty$ bound on the ratio between their densities, Wasserstein distances,
and Kullback--Leibler divergence. In particular, an extension of the
Holley--Stroock perturbation lemma for the log-Sobolev inequality is obtained,
and the dependence on the perturbation parameter is improved from linear to
logarithmic. Second, the equivalence of Transport-Entropy inequalities with
different cost-functions is verified, by obtaining a reverse Jensen type
inequality. The main tool used is a previous precise result on the equivalence
between concentration and isoperimetric inequalities in the described setting.
Of independent interest is a new dimension independent characterization of
Transport-Entropy inequalities with respect to the 1-Wasserstein distance,
which does not assume any curvature lower bound.

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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat