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

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

(2015) Luigi Ambrosio et al.   ANNALS OF PROBABILITY

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

Sharp isoperimetric inequalities and model spaces for the Curvature-Dimension-Diameter condition

(2015) Emanuel Milman   JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY

Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows

(2015) Nicola Gigli et al.   PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY

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

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

Complemented Brunn–Minkowski inequalities and isoperimetry for homogeneous and non-homogeneous measures

(2014) Emanuel Milman et al.   ADVANCES IN MATHEMATICS

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

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

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

Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions

(2013) Michael Eichmair et al.   INVENTIONES MATHEMATICAE

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

Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications

(2012) Tobias Colding et al.   ANNALS OF MATHEMATICS

A Selection Principle for the Sharp Quantitative Isoperimetric Inequality

(2012) Marco Cicalese et al.   ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS

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

(2012) Nicola Gigli   GEOMETRIC AND FUNCTIONAL ANALYSIS

Local curvature-dimension condition implies measure-contraction property

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

Local Poincaré inequalities from stable curvature conditions on metric spaces

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

A mass transportation approach to quantitative isoperimetric inequalities

(2010) A. Figalli et al.   INVENTIONES MATHEMATICAE

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

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

The sharp quantitative isoperimetric inequality

(2009) Nicola Fusco et al.   ANNALS OF MATHEMATICS

Ricci curvature for metric-measure spaces via optimal transport

(2009) John Lott et al.   ANNALS OF MATHEMATICS

Finsler interpolation inequalities

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