Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds

2016/11/19 by Fabio Cavalletti, Andrea Mondino · 15 citations
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Nonlinear Partial Differential Equations

paper · doi:10.1007/s00222-016-0700-6

Citations

• Ricci curvature for metric-measure spaces via optimal transport
• On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces
• Lower Bounds on Ricci Curvature and the Almost Rigidity of Warped Products
• Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications
• An optimal Poincaré inequality for convex domains

Cited by

• The globalization theorem for the Curvature-Dimension condition
• One dimensional 𝖱𝖢𝖣 spaces always satisfy the regular Weyl’s law
• Failure of curvature-dimension conditions on sub-Riemannian manifolds via tangent isometries
• On the structure of \mathrm RCD spaces with upper curvature bounds
• Isoperimetric problems and lower bounds on curvature
• An Information-Theoretic Route to Isoperimetric Inequalities via Heat Flow and Entropy Dissipation
• Comparison estimates on nonsmooth spaces with integrable Ricci lower bounds via localization
• Almost-Riemannian manifolds do not satisfy the curvature-dimension condition
• Cheng's eigenvalue comparison on metric measure spaces and applications
• Sharp Cheeger-Buser Type Inequalities in RCD ( K , ∞ ) Spaces. [europepmc]
• Optimal transport of vector measures. [europepmc]
• Curvature-dimension conditions under time change. [europepmc]
• Almost-Riemannian manifolds do not satisfy the curvature-dimension condition. [europepmc]
• Ricci curvature bounds and rigidity for non-smooth Riemannian and semi-Riemannian metrics. [europepmc]
• Hawking's Singularity Theorem for Lipschitz Lorentzian Metrics. [europepmc]