We prove the equivalence of the curvature-dimension bounds of Lott–Sturm–Villani (via
entropy and optimal transport) and of Bakry–Émery (via energy and Γ _2 Γ 2-calculus) in …

The main result of this article states that the (K, N)-cone over some metric measure space
satisfies the reduced Riemannian curvature-dimension condition RCD⁎(KN, N+ 1) if and …

Some of the many good features of the Riemannian curvature-dimension condition is that it
corresponds, in the setting of smooth Riemannian manifolds, to a standard lower Ricci …

Consider an essentially nonbranching metric measure space with the measure contraction
property of Ohta and Sturm, or with a Ricci curvature lower bound in the sense of Lott, Sturm …

We study $\mathsf {RCD} $-spaces $(X, d,\mathfrak {m}) $ with group actions by isometries
preserving the reference measure $\mathfrak {m} $ and whose orbit space has dimension …

In this note we prove the Heintze-Karcher inequality in the context of essentially non-
branching metric measure spaces satisfying a lower Ricci curvature bound in the sense of …

Vers l'an 2000, le développement rapide de la théorie du transport optimal menait à la
découverte de liens étroits entre courbure de Ricci, entropie de Boltzmann et transport de …

We study the Wasserstein barycenter problem in the setting of non-compact, non-smooth
extended metric measure spaces. We introduce a couple of new concepts and obtain the …

In this article we study stability and compactness wrt measured Gromov-Hausdorff
convergence of smooth metric measure spaces with integral Ricci curvature bounds. More …

We introduce a notion of doubly warped product of weighted graphs that is consistent with
the doubly warped product in the Riemannian setting. We establish various discrete Bakry …