On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces

[1]  Angelo Profeta.  The Sharp Sobolev Inequality on Metric Measure Spaces with Lower Ricci Curvature Bounds , 2015 .

[2]  L. Ambrosio,et al.  Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds , 2012, 1209.5786.

[3]  L. Ambrosio,et al.  Riemannian Ricci curvature lower bounds in metric measure spaces with -finite measure , 2012, 1207.4924.

[4]  Arnaud Guillin,et al.  Dimensional contraction via Markov transportation distance , 2013, J. Lond. Math. Soc..

[5]  L. Ambrosio,et al.  Metric measure spaces with Riemannian Ricci curvature bounded from below , 2011, 1109.0222.

[6]  Nicola Gigli,et al.  Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below , 2011, 1106.2090.

[7]  Karl-Theodor Sturm,et al.  Ricci Bounds for Euclidean and Spherical Cones , 2010, 1003.2114.

[8]  Kazumasa Kuwada.  Space-time Wasserstein controls and Bakry–Ledoux type gradient estimates , 2013, 1308.5471.

[9]  Characterizations of Bounded Ricci Curvature on Smooth and NonSmooth Spaces , 2013, 1306.6512.

[10]  A. Mondino,et al.  Li–Yau and Harnack type inequalities in RCD∗(K,N) metric measure spaces , 2013, 1306.0494.

[11]  L. Ambrosio,et al.  A User’s Guide to Optimal Transport , 2013 .

[12]  Karl-Theodor Sturm,et al.  Non-branching geodesics and optimal maps in strong C D ( K , ∞ ) -spaces , 2013 .

[13]  C. Ketterer.  Ricci curvature bounds for warped products , 2012, 1209.1325.

[14]  P. Koskela,et al.  Geometry and Analysis of Dirichlet forms , 2012, 1208.4955.

[15]  Non-branching geodesics and optimal maps in strong CD(K,{\infty})-spaces , 2012 .

[16]  N. Gigli.  On the differential structure of metric measure spaces and applications , 2012, 1205.6622.

[17]  Karl-Theodor Sturm,et al.  Local curvature-dimension condition implies measure-contraction property , 2011, 1112.4991.

[18]  T. Rajala.  Local Poincaré inequalities from stable curvature conditions on metric spaces , 2011, 1107.4842.

[19]  Karl-Theodor Sturm,et al.  Bochner-Weitzenb\"ock formula and Li-Yau estimates on Finsler manifolds , 2011, 1105.0983.

[20]  Ricci Bounds for Euclidean and Spherical Cones (revised/extended version) , 2011, 1103.0197.

[21]  Feng-Yu Wang.  Equivalent semigroup properties for the curvature-dimension condition , 2010, 1012.5686.

[22]  Xiping Zhu,et al.  Yau's gradient estimates on Alexandrov spaces , 2010, 1012.4233.

[23]  Nicola Gigli,et al.  On the heat flow on metric measure spaces: existence, uniqueness and stability , 2010 .

[24]  Nicola Gigli,et al.  Heat Flow on Alexandrov Spaces , 2010, 1008.1319.

[25]  Anton Petrunin,et al.  Alexandrov meets Lott-Villani-Sturm , 2010, 1003.5948.

[26]  Karl-Theodor Sturm,et al.  Localization and Tensorization Properties of the Curvature-Dimension Condition for Metric Measure Spaces , 2010, 1003.2116.

[27]  Xiping Zhu,et al.  Ricci Curvature on Alexandrov spaces and Rigidity Theorems , 2009, 0912.3190.

[28]  Kazumasa Kuwada,et al.  Duality on gradient estimates and Wasserstein controls , 2009, 0910.1741.

[29]  Shin-Ichi Ohta,et al.  Finsler interpolation inequalities , 2009 .

[30]  C. Villani.  Optimal Transport: Old and New , 2008 .

[31]  Sara Daneri,et al.  Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance , 2008, SIAM J. Math. Anal..

[32]  Michel Ledoux,et al.  A logarithmic Sobolev form of the Li-Yau parabolic inequality , 2006 .

[33]  Karl-Theodor Sturm,et al.  On the geometry of metric measure spaces. II , 2006 .

[34]  Karl-Theodor Sturm,et al.  On the geometry of metric measure spaces , 2006 .

[35]  L. Ambrosio,et al.  Gradient Flows: In Metric Spaces and in the Space of Probability Measures , 2005 .

[36]  Felix Otto,et al.  Eulerian Calculus for the Contraction in the Wasserstein Distance , 2005, SIAM J. Math. Anal..

[37]  C. Villani,et al.  Ricci curvature for metric-measure spaces via optimal transport , 2004, math/0412127.

[38]  Arcwise Isometries,et al.  A Course in Metric Geometry , 2001 .

[39]  Cédric Villani,et al.  A short proof of the "Concavity of entropy power" , 2000, IEEE Trans. Inf. Theory.

[40]  C. Villani,et al.  Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality , 2000 .

[41]  Pekka Koskela,et al.  Sobolev met Poincaré , 2000 .

[42]  D. Kinderlehrer,et al.  THE VARIATIONAL FORMULATION OF THE FOKKER-PLANCK EQUATION , 1996 .

[43]  D. Bakry.  L'hypercontractivité et son utilisation en théorie des semigroupes , 1994 .

[44]  Amir Dembo,et al.  Information theoretic inequalities , 1991, IEEE Trans. Inf. Theory.

[45]  E. Davies,et al.  Heat kernels and spectral theory , 1989 .

[46]  P. Bérard.  Spectral Geometry: Direct and Inverse Problems , 1986 .

[47]  S. Yau,et al.  On the parabolic kernel of the Schrödinger operator , 1986 .