Isoperimetric inequalities on weighted manifolds with boundary

DOI10.1134/S1064562415050063zbMath1331.49064OpenAlexW2282042976MaRDI QIDQ906088

Alexander V. Kolesnikov, Emanuel Milman

Publication date: 29 January 2016

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

Full work available at URL: https://doi.org/10.1134/s1064562415050063

zbMATH Keywords

isoperimetric inequalitiesweighted manifoldsPoincaré-type inequalitiesBrunn-Minkowski-type inequalities

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (4)

Dimensional variance inequalities of Brascamp-Lieb type and a local approach to dimensional Prékopa's theorem ⋮ Rigidity phenomena in manifolds with boundary under a lower weighted Ricci curvature bound ⋮ A local proof of the dimensional Prékopa's theorem ⋮ Lower bound estimates for the first eigenvalue of the weighted \(p\)-Laplacian on smooth metric measure spaces

Cites Work

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• Extension of Reilly formula with applications to eigenvalue estimates for drifting Laplacians
• Weighted Poincaré-type inequalities for Cauchy and other convex measures
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• Sharp isoperimetric inequalities and model spaces for the curvature-dimension-diameter condition
• FROM THE BRUNN–MINKOWSKI INEQUALITY TO A CLASS OF POINCARÉ-TYPE INEQUALITIES
• Rigidity of compact manifolds with boundary and nonnegative Ricci curvature

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