Equivalence between dimensional contractions in Wasserstein distance and the curvature-dimension condition

DOI10.2422/2036-2145.201611_009zbMath1406.58020arXiv1510.07793OpenAlexW1859871475MaRDI QIDQ4579903

Kazumasa Kuwada, Arnaud Guillin, François Bolley, Ivan Gentil

Publication date: 10 August 2018

Published in: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.07793

zbMATH Keywords

metric measure spaceBochner inequalityWasserstein contraction property

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Variational inequalities (global problems) in infinite-dimensional spaces (58E35) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Methods of local Riemannian geometry (53B21)

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Convexity and regularity properties for entropic interpolations ⋮ Dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities ⋮ Dynamical aspects of the generalized Schrödinger problem via Otto calculus -- a heuristic point of view ⋮ Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces ⋮ Super-Ricci flows and improved gradient and transport estimates ⋮ Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups

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