Optimal transport, gradient estimates, and pathwise Brownian coupling on spaces with variable Ricci bounds

DOI10.1016/j.matpur.2021.01.002zbMath1459.58013arXiv1906.09186OpenAlexW3119736021MaRDI QIDQ2656179

Karl-Theodor Sturm, Mathias Braun, Karen Habermann

Publication date: 10 March 2021

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.09186

zbMATH Keywords

gradient estimateRicci curvaturecouplingoptimal transportBakry-Émery estimate

Mathematics Subject Classification ID

Dirichlet forms (31C25) Heat equation (35K05) Diffusion processes (60J60) Diffusion processes and stochastic analysis on manifolds (58J65) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Optimal transportation (49Q22) Dirichlet form methods in Markov processes (60J46)

Related Items (8)

Tamed spaces -- Dirichlet spaces with distribution-valued Ricci bounds ⋮ Heat flow on 1-forms under lower Ricci bounds. Functional inequalities, spectral theory, and heat kernel ⋮ Self-improvement of the Bakry-Emery criterion for Poincaré inequalities and Wasserstein contraction using variable curvature bounds ⋮ Metric measure spaces and synthetic Ricci bounds: fundamental concepts and recent developments ⋮ A synthetic null energy condition ⋮ Mini-workshop: Variable curvature bounds, analysis and topology on Dirichlet spaces. Abstracts from the mini-workshop held December 5--11, 2021 (hybrid meeting) ⋮ A Feynman-Kac approach for logarithmic Sobolev inequalities ⋮ Heat flow regularity, Bismut-Elworthy-Li's derivative formula, and pathwise couplings on Riemannian manifolds with Kato bounded Ricci curvature

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