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

Metric measure spaces with Riemannian Ricci curvature bounded from below

(2014) Luigi Ambrosio et al.   DUKE MATHEMATICAL JOURNAL

Decomposition of Geodesics in the Wasserstein Space and the Globalization Problem

(2014) Fabio Cavalletti   GEOMETRIC AND FUNCTIONAL ANALYSIS

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

Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in $RCD (K, \infty)$ metric measure spaces

(2013) Giuseppe Savaré   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

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

(2013) Luigi Ambrosio et al.   INVENTIONES MATHEMATICAE

A PDE approach to nonlinear potential theory in metric measure spaces

(2013) Nicola Gigli et al.   JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES

Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm

(2012) Tapio Rajala   JOURNAL OF FUNCTIONAL ANALYSIS

Local Poincaré inequalities from stable curvature conditions on metric spaces

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

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

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

Riesz meets Sobolev

(2010) Thierry Coulhon et al.   COLLOQUIUM MATHEMATICUM

Ricci curvature for metric-measure spaces via optimal transport

(2009) John Lott et al.   ANNALS OF MATHEMATICS

The Wasserstein Gradient Flow of the Fisher Information and the Quantum Drift-diffusion Equation

(2008) Ugo Gianazza et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance

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