Gaussian-type isoperimetric inequalities in \(\mathsf{RCD}(K,\infty)\) probability spaces for positive \(K\)

DOI10.4171/RLM/745zbMath1351.49056arXiv1605.02852OpenAlexW2354708855MaRDI QIDQ333009

Luigi Ambrosio, Andrea Mondino

Publication date: 9 November 2016

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.02852

zbMATH Keywords

isoperimetric inequalityRicci curvatureGaussian measuresmetric geometrymetric analysis

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Variational problems in a geometric measure-theoretic setting (49Q20) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (11)

Diffusion, optimal transport and Ricci curvature ⋮ Needle decompositions and isoperimetric inequalities in Finsler geometry ⋮ Stability of eigenvalues and observable diameter in RCD\((1, \infty)\) spaces ⋮ Sharp Cheeger-buser type inequalities in \(\mathsf{RCD}(K,\infty)\) spaces ⋮ Isoperimetric rigidity and distributions of 1-Lipschitz functions ⋮ Nonlinear geometric analysis on Finsler manifolds ⋮ Rigidity of some functional inequalities on RCD spaces ⋮ Rigidity for the isoperimetric inequality of negative effective dimension on weighted Riemannian manifolds ⋮ The equality case in Cheeger's and Buser's inequalities on \(\mathsf{RCD}\) spaces ⋮ Quantitative estimates for the Bakry-Ledoux isoperimetric inequality ⋮ Cones over metric measure spaces and the maximal diameter theorem

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