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

Sharp spectral gaps on metric measure spaces

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

Lower bound estimates for the first eigenvalue of the weighted p -Laplacian on smooth metric measure spaces

(2016) Yu-Zhao Wang et al.   DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS

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

(2016) Fabio Cavalletti et al.   INVENTIONES MATHEMATICAE

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

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

(2015) Emanuel Milman   JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY

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

(2015) Angelo Profeta   POTENTIAL ANALYSIS

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

Sharp estimates on the first eigenvalue of the $$p$$ p -Laplacian with negative Ricci lower bound

(2014) Aaron Naber et al.   MATHEMATISCHE ZEITSCHRIFT

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

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

(2013) Luigi Ambrosio et al.   INVENTIONES MATHEMATICAE

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

(2012) Tobias Colding et al.   ANNALS OF MATHEMATICS

From log Sobolev to Talagrand: A quick proof

(2012) Nicola Gigli et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Local curvature-dimension condition implies measure-contraction property

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

Sharp estimate on the first eigenvalue of the -Laplacian

(2012) Daniele Valtorta   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

First eigenvalue of the p-Laplace operator along the Ricci flow

(2010) Jia-Yong Wu et al.   ANNALS OF GLOBAL ANALYSIS AND GEOMETRY

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

Finsler interpolation inequalities

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

On the role of convexity in isoperimetry, spectral gap and concentration

(2009) Emanuel Milman   INVENTIONES MATHEMATICAE