Gradient flows for semiconvex functions on metric measure spaces – existence, uniqueness, and Lipschitz continuity

DOI10.1090/proc/14061zbMath1395.49038arXiv1410.3966OpenAlexW2963355562WikidataQ125853156 ScholiaQ125853156MaRDI QIDQ4577172

Karl-Theodor Sturm

Publication date: 17 July 2018

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.3966

zbMATH Keywords

gradient flowLipschitz continuitymetric measure space

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Variational inequalities (global problems) in infinite-dimensional spaces (58E35) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (8)

Obata's rigidity theorem for metric measure spaces ⋮ Regularity of Lagrangian flows over \(\operatorname{RCD}^*(K, N)\) spaces ⋮ CD meets CAT ⋮ Neumann heat flow and gradient flow for the entropy on non-convex domains ⋮ Distribution-valued Ricci bounds for metric measure spaces, singular time changes, and gradient estimates for Neumann heat flows ⋮ DC calculus ⋮ Gradient flows and evolution variational inequalities in metric spaces. I: structural properties ⋮ Curvature-dimension conditions under time change

Cites Work

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• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• Open map theorem for metric spaces

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