The Sharp Sobolev Inequality on Metric Measure Spaces with Lower Ricci Curvature Bounds

Metric measure spaces with Riemannian Ricci curvature bounded from below

(2014) Luigi Ambrosio et al.   DUKE MATHEMATICAL JOURNAL

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

Li–Yau and Harnack type inequalities in metric measure spaces

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

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

Ricci curvature for metric-measure spaces via optimal transport

(2009) John Lott et al.   ANNALS OF MATHEMATICS