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

Bakry–Émery curvature-dimension condition and Riemannian Ricci curvature bounds

(2015) Luigi Ambrosio et al.   ANNALS OF PROBABILITY

Metric measure spaces with Riemannian Ricci curvature bounded from below

(2014) Luigi Ambrosio et al.   DUKE MATHEMATICAL JOURNAL

On the Bakry–Émery Condition, the Gradient Estimates and the Local-to-Global Property of $$\mathsf{RCD}^*(K,N)$$ RCD ∗ ( K , N ) Metric Measure Spaces

(2014) Luigi Ambrosio et al.   JOURNAL OF GEOMETRIC ANALYSIS

Dimensional contraction via Markov transportation distance

(2014) François Bolley et al.   JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

Bochner–Weitzenböck formula and Li–Yau estimates on Finsler manifolds

(2013) Shin-ichi Ohta et al.   ADVANCES IN MATHEMATICS

Non-branching geodesics and optimal maps in strong $$CD(K,\infty )$$ C D ( K , ∞ ) -spaces

(2013) Tapio Rajala et al.   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Ricci curvature on Alexandrov spaces and rigidity theorems

(2013) Hui-Chun Zhang et al.   COMMUNICATIONS IN ANALYSIS AND GEOMETRY

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

(2013) Luigi Ambrosio et al.   INVENTIONES MATHEMATICAE

Ricci curvature bounds for warped products

(2013) Christian Ketterer   JOURNAL OF FUNCTIONAL ANALYSIS

Li–Yau and Harnack type inequalities in metric measure spaces

(2013) Nicola Garofalo et al.   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Geometry and analysis of Dirichlet forms

(2012) Pekka Koskela et al.   ADVANCES IN MATHEMATICS

Heat Flow on Alexandrov Spaces

(2012) Nicola Gigli et al.   COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

Local curvature-dimension condition implies measure-contraction property

(2012) Fabio Cavalletti et al.   JOURNAL OF FUNCTIONAL ANALYSIS

Equivalent semigroup properties for the curvature-dimension condition

(2011) Feng-Yu Wang   BULLETIN DES SCIENCES MATHEMATIQUES

Local Poincaré inequalities from stable curvature conditions on metric spaces

(2011) Tapio Rajala   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Duality on gradient estimates and Wasserstein controls

(2010) Kazumasa Kuwada   JOURNAL OF FUNCTIONAL ANALYSIS

Localization and tensorization properties of the curvature-dimension condition for metric measure spaces

(2010) Kathrin Bacher et al.   JOURNAL OF FUNCTIONAL ANALYSIS

Ricci curvature for metric-measure spaces via optimal transport

(2009) John Lott et al.   ANNALS OF MATHEMATICS

On the heat flow on metric measure spaces: existence, uniqueness and stability

(2009) Nicola Gigli   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Finsler interpolation inequalities

(2009) Shin-ichi Ohta   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance

(2008) Sara Daneri et al.   SIAM JOURNAL ON MATHEMATICAL ANALYSIS