Non-compact $$\text {RCD}(0,N)$$ RCD ( 0 , N ) Spaces with Linear Volume Growth

Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds

(2017) Fabio Cavalletti et al.   GEOMETRY & TOPOLOGY

Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds

(2017) Fabio Cavalletti et al.   GEOMETRY & TOPOLOGY

Local Li–Yau’s estimates on RCD $$^*(K,N)$$ ∗ ( K , N ) metric measure spaces

(2016) Hui-Chun Zhang et al.   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

Sharp spectral gaps on metric measure spaces

(2016) Yin Jiang et al.   CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS

From volume cone to metric cone in the nonsmooth setting

(2016) Guido De Philippis et al.   GEOMETRIC AND FUNCTIONAL ANALYSIS

Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds

(2016) Fabio Cavalletti et al.   INVENTIONES MATHEMATICAE

Existence and uniqueness of optimal transport maps

(2015) Fabio Cavalletti et al.   ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE

Cones over metric measure spaces and the maximal diameter theorem

(2015) Christian Ketterer   JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES

Optimal Maps and Exponentiation on Finite-Dimensional Spaces with Ricci Curvature Bounded from Below

(2015) Nicola Gigli et al.   JOURNAL OF GEOMETRIC ANALYSIS

Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma $-finite measure

(2015) Luigi Ambrosio et al.   TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

Metric measure spaces with Riemannian Ricci curvature bounded from below

(2014) Luigi Ambrosio et al.   DUKE MATHEMATICAL JOURNAL

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

(2014) Matthias Erbar et al.   INVENTIONES MATHEMATICAE

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

Monge problem in metric measure spaces with Riemannian curvature-dimension condition

(2014) Fabio Cavalletti   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

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

The Monge Problem for Distance Cost in Geodesic Spaces

(2013) Stefano Bianchini et al.   COMMUNICATIONS IN MATHEMATICAL PHYSICS

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

Li–Yau and Harnack type inequalities in metric measure spaces

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

OPTIMAL MAPS IN NON BRANCHING SPACES WITH RICCI CURVATURE BOUNDED FROM BELOW

(2012) Nicola Gigli   GEOMETRIC AND FUNCTIONAL ANALYSIS

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

Ricci curvature for metric-measure spaces via optimal transport

(2009) John Lott et al.   ANNALS OF MATHEMATICS