Concentration and isoperimetry are equivalent assuming curvature lower bound

DOI10.1016/j.crma.2008.11.014zbMath1156.53022OpenAlexW2070791491MaRDI QIDQ1000658

Emanuel Milman

Publication date: 10 February 2009

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.2008.11.014

zbMATH Keywords

Bakry-Émery curvature tensormeasure-metric-space

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Global Riemannian geometry, including pinching (53C20)

Related Items (4)

Properties of isoperimetric, functional and transport-entropy inequalities via concentration ⋮ Isoperimetric Hardy Type and Poincaré Inequalities on Metric Spaces ⋮ Pointwise symmetrization inequalities for Sobolev functions and applications ⋮ Isoperimetric and concentration inequalities: equivalence under curvature lower bound

Cites Work

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• Uniform tail-decay of Lipschitz functions implies Cheeger's isoperimetric inequality under convexity assumptions
• Mass transport and variants of the logarithmic Sobolev inequality
• Logarithmic Sobolev inequalities on noncompact Riemannian manifolds
• Isoperimetric and analytic inequalities for log-concave probability measures
• Levels of concentration between exponential and Gaussian
• Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator
• An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies
• OPTIMAL INTEGRABILITY CONDITION FOR THE LOG-SOBOLEV INEQUALITY
• A note on the isoperimetric constant

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