Riemannian metrics on \(\mathbb{R}^n\) and Sobolev-type inequalities

DOI10.1134/S1064562416050082zbMath1360.53037OpenAlexW2555980083WikidataQ115247461 ScholiaQ115247461MaRDI QIDQ512494

Alexander V. Kolesnikov, Emanuel Milman

Publication date: 27 February 2017

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562416050082

zbMATH Keywords

Poincaré-type inequalitymeasureHessian metricweighted manifoldBakry-Emery tensorconical measureproduct metricsRiemanian metric

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Global Riemannian geometry, including pinching (53C20)

Cites Work

• Poincaré inequalities and moment maps
• Hessian metrics, \(CD(K, N)\)-spaces, and optimal transportation of log-concave measures
• Isoperimetric and concentration inequalities: equivalence under curvature lower bound
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• Moment measures
• Dimensional variance inequalities of Brascamp-Lieb type and a local approach to dimensional Prékopa's theorem
• The Monge-Kantorovich problem: achievements, connections, and perspectives
• Logarithmically-Concave Moment Measures I
• Remarks on the KLS Conjecture and Hardy-Type Inequalities

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