In this paper, we introduce a synthetic notion of Riemannian Ricci bounds from below for
metric measure spaces (X, d, m) which is stable under measured Gromov–Hausdorff …

This paper is devoted to a deeper understanding of the heat flow and to the refinement of
calculus tools on metric measure spaces (X,d,m). Our main results are: A general study of …

The main goals of this paper are:(i) To develop an abstract differential calculus on metric
measure spaces by investigating the duality relations between differentials and gradients of …

In the recent paper [24] the Cheeger-Colding-Gromoll splitting theorem has been
generalized to the abstract class of metric measure spaces with Riemannian Ricci curvature …

Let K be an irreducible and reversible Markov kernel on a finite set X. We construct a metric
W on the set of probability measures on X and show that with respect to this metric, the law …

The aim of the present paper is to bridge the gap between the Bakry–Émery and the Lott–
Sturm–Villani approaches to provide synthetic and abstract notions of lower Ricci curvature …

We study a new notion of Ricci curvature that applies to Markov chains on discrete spaces.
This notion relies on geodesic convexity of the entropy and is analogous to the one …

Abstract We extend Cordero-Erausquin et al.'s Riemannian Borell–Brascamp–Lieb
inequality to Finsler manifolds. Among applications, we establish the equivalence between …

We prove that the linear heat flow in a RCD (K,\infty) metric measure space (X, d, m) satisfies
a contraction property with respect to every L^ p-Kantorovich-Rubinstein-Wasserstein …

The main aim of this book is to present recent developments of comparison geometry and
geometric analysis on Finsler manifolds in an accessible way to students and researchers …