Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-improvement of the Bakry-\'Emery condition and Wasserstein
  contraction of the heat flow in RCD(K,\infty) metric measure spaces   We prove that the linear heat flow in a RCD(K,\infty) metric measure space
(X,d,m) satisfies a contraction property with respect to every
L^p-Kantorovich-Rubinstein-Wasserstein distance. In particular, we obtain a
precise estimate for the optimal W_\infty-coupling between two fundamental
solutions in terms of the distance of the initial points.
  The result is a consequence of the equivalence between the RCD(K,\infty)
lower Ricci bound and the corresponding Bakry-\'Emery condition for the
canonical Cheeger-Dirichlet form in (X,d,m). The crucial tool is the extension
to the non-smooth metric measure setting of the Bakry's argument, that allows
to improve the commutation estimates between the Markov semigroup and the
Carr\'e du Champ associated to the Dirichlet form. This extension is based on a
new a priori estimate and a capacitary argument for regular and tight Dirichlet
forms that are of independent interest.

1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org