Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma $-finite measure, Transactions of the American Mathematical Society, vol.367, issue.7, pp.4661-4701, 2015. ,
DOI : 10.1090/S0002-9947-2015-06111-X
URL : https://hal.archives-ouvertes.fr/hal-00769370
Gradient flows in metric spaces and in the space of probability measures, Lectures in Math. ETH Zürich. Birkhäuser, 2008. ,
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below, Inventiones mathematicae, vol.196, issue.1???2, pp.289-391, 2013. ,
DOI : 10.1007/s00222-013-0456-1
URL : https://hal.archives-ouvertes.fr/hal-00769378
Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces, Revista Matem??tica Iberoamericana, vol.29, issue.3, pp.969-996, 2013. ,
DOI : 10.4171/RMI/746
URL : https://hal.archives-ouvertes.fr/hal-00769374
Metric measure spaces with Riemannian Ricci curvature bounded from below, Duke Mathematical Journal, vol.163, issue.7, pp.1405-1490, 2014. ,
DOI : 10.1215/00127094-2681605
URL : https://hal.archives-ouvertes.fr/hal-00769376
Bakry?????mery curvature-dimension condition and Riemannian Ricci curvature bounds, The Annals of Probability, vol.43, issue.1, pp.339-404, 2015. ,
DOI : 10.1214/14-AOP907
URL : http://arxiv.org/abs/1209.5786
Diffusions hypercontractives In Séminaire de probabilités, XIX, Lecture Notes in Math, vol.84, issue.1123, pp.177-206, 1983. ,
Analysis and geometry of Markov diffusion operators, 2014. ,
DOI : 10.1007/978-3-319-00227-9
URL : https://hal.archives-ouvertes.fr/hal-00929960
On Harnack inequalities and optimal transportation, Ann. Sc. Norm. Super. Pisa, Cl. Sci, vol.14, issue.3, pp.705-727, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-00742654
Dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01171361
Dimensional contraction via Markov transportation distance, Journal of the London Mathematical Society, vol.135, issue.1, pp.309-332, 2014. ,
DOI : 10.1112/jlms/jdu027
URL : https://hal.archives-ouvertes.fr/hal-00808717
A course in metric geometry, volume 33 of Grad. studies math, Amer. Math. Soc, 2001. ,
On the equivalence of the entropic curvature-dimension condition and Bochner???s inequality on metric measure spaces, Inventiones mathematicae, vol.91, issue.3, pp.993-1071, 2015. ,
DOI : 10.1007/s00222-014-0563-7
Heat Flow on Alexandrov Spaces, Communications on Pure and Applied Mathematics, vol.91, issue.3, pp.307-331, 2013. ,
DOI : 10.1002/cpa.21431
URL : https://hal.archives-ouvertes.fr/hal-00769390
The Variational Formulation of the Fokker--Planck Equation, SIAM Journal on Mathematical Analysis, vol.29, issue.1, pp.1-17, 1998. ,
DOI : 10.1137/S0036141096303359
Duality on gradient estimates and Wasserstein controls, Journal of Functional Analysis, vol.258, issue.11, pp.3758-3774, 2010. ,
DOI : 10.1016/j.jfa.2010.01.010
Space-time Wasserstein controls and Bakry???Ledoux type gradient estimates, Calculus of Variations and Partial Differential Equations, vol.135, issue.6???7, pp.127-161, 2015. ,
DOI : 10.1007/s00526-014-0781-2
Dimension-free Harnack inequalities on RCD (K, ?) spaces ,
Characterization of absolutely continuous curves in Wasserstein spaces, Calculus of Variations and Partial Differential Equations, vol.58, issue.7, pp.85-120, 2007. ,
DOI : 10.1007/s00526-006-0032-2
Ricci curvature for metric-measure spaces via optimal transport, Annals of Mathematics, vol.169, issue.3, pp.903-991, 2009. ,
DOI : 10.4007/annals.2009.169.903
Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality, Journal of Functional Analysis, vol.173, issue.2, pp.361-400, 2000. ,
DOI : 10.1006/jfan.1999.3557
Eulerian Calculus for the Contraction in the Wasserstein Distance, SIAM Journal on Mathematical Analysis, vol.37, issue.4, pp.1227-1255, 2005. ,
DOI : 10.1137/050622420
Self-improvement of the Bakry-??mery condition and Wasserstein contraction of the heat flow in $RCD (K, \infty)$ metric measure spaces, Discrete and Continuous Dynamical Systems, vol.34, issue.4, pp.1641-1661, 2014. ,
DOI : 10.3934/dcds.2014.34.1641
On the geometry of metric measure spaces. II, Acta Mathematica, vol.196, issue.1, pp.65-177, 2006. ,
DOI : 10.1007/s11511-006-0003-7
Optimal transport, Old and new, 2009. ,
Transport inequalities, gradient estimates, entropy and Ricci curvature, Communications on Pure and Applied Mathematics, vol.108, issue.7, pp.923-940, 2005. ,
DOI : 10.1002/cpa.20060
Functional Inequalities, Markov Processes, and Spectral Theory, 2004. ,
Equivalent semigroup properties for the curvature-dimension condition, Bulletin des Sciences Math??matiques, vol.135, issue.6-7, pp.803-815, 2011. ,
DOI : 10.1016/j.bulsci.2011.07.005