Curvature-dimension conditions under time change

DOI10.1007/s10231-021-01138-xzbMath1489.53059OpenAlexW3191107976MaRDI QIDQ2118042

Karl-Theodor Sturm, Bang-Xian Han

Publication date: 22 March 2022

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-021-01138-x

zbMATH Keywords

Dirichlet formtime changemetric measure spacecurvature-dimension conditionBakry-Émery theory

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Potential theory on fractals and metric spaces (31E05)

Related Items (1)

Metric measure spaces and synthetic Ricci bounds: fundamental concepts and recent developments

Cites Work

• Unnamed Item
• Unnamed Item
• On the Bakry-Émery condition, the gradient estimates and the local-to-global property of \(\mathrm{RCD}^*(K,N)\) metric measure spaces
• Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in \(\text{RCD}(K, \infty)\) metric measure spaces
• Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
• On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
• Dirichlet forms and symmetric Markov processes.
• Intrinsic geometry and analysis of diffusion processes and \(L^{\infty}\)-variational problems
• Ricci tensor for diffusion operators and curvature-dimension inequalities under conformal transformations and time changes
• Ricci tensor on \(\mathrm{RCD}^\ast(K,N)\) spaces
• Neumann heat flow and gradient flow for the entropy on non-convex domains
• Analysis on local Dirichlet spaces. II: Upper Gaussian estimates for the fundamental solutions of parabolic equations
• Distribution-valued Ricci bounds for metric measure spaces, singular time changes, and gradient estimates for Neumann heat flows
• The globalization theorem for the curvature-dimension condition
• Conformal transformation on metric measure spaces
• Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds
• Ricci curvature for metric-measure spaces via optimal transport
• 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
• New formulas for the Laplacian of distance functions and applications
• On the differential structure of metric measure spaces and applications
• Gradient flows for semiconvex functions on metric measure spaces – existence, uniqueness, and Lipschitz continuity
• Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below
• An overview of L1 Optimal Transportation on metric measure spaces

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