A curvature-dimension condition for metric measure spaces

DOI10.1016/J.CRMA.2005.11.008zbMath1094.53030OpenAlexW1966575973MaRDI QIDQ817881

Karl-Theodor Sturm

Publication date: 20 March 2006

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.2005.11.008

zbMATH Keywords

Ricci curvaturemetric measure spaces

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Spaces of measures, convergence of measures (28A33)

Related Items (11)

Ricci curvature, isoperimetry and a non-additive entropy ⋮ A global Poincaré inequality on graphs via a conical curvature-dimension condition ⋮ Positive scalar curvature with skeleton singularities ⋮ The Yamabe problem for distributional curvature ⋮ Weak scalar curvature lower bounds along Ricci flow ⋮ The Wasserstein geometry of nonlinear σ models and the Hamilton–Perelman Ricci flow ⋮ Sewing Riemannian manifolds with positive scalar curvature ⋮ Sharp estimates for the principal eigenvalue of the \(p\)-operator ⋮ On the geometry of metric measure spaces. II ⋮ A polyhedron comparison theorem for 3-manifolds with positive scalar curvature ⋮ Spectral stability of metric-measure Laplacians

Cites Work

• Unnamed Item
• Some new results on eigenvectors via dimension, diameter, and Ricci curvature
• A Riemannian interpolation inequality à la Borell, Brascamp and Lieb
• Generalized Ricci bounds and convergence of metric measure spaces
• Convex functionals of probability measures and nonlinear diffusions on manifolds
• Ricci curvature for metric-measure spaces via optimal transport

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