Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds

DOI10.1016/j.crma.2007.06.018zbMath1125.53064OpenAlexW2089399938MaRDI QIDQ2643117

Giuseppe Savaré

Publication date: 23 August 2007

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2007.06.018

zbMATH Keywords

Fokker-Planck equationgeodesicprobability measuresmetric measure spaces

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Markov semigroups and applications to diffusion processes (47D07) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Probabilistic measure theory (60A10) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Direct methods ((G)-spaces of Busemann, etc.) (53C70)

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Cites Work

• Gradient flows on nonpositively curved metric spaces and harmonic maps
• Ricci curvature for metric-measure spaces via optimal transport
• On the geometry of metric measure spaces. I
• The Variational Formulation of the Fokker--Planck Equation
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