Exponential concentration in terms of Gromov-Ledoux's expansion coefficients on a metric measure space and its upper diameter bound satisfying volume doubling

zbMath1504.53058MaRDI QIDQ2080646

Ushio Tanaka

Publication date: 10 October 2022

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/osaka-journal-of-mathematics/volume-59/issue-4/Exponential-Concentration-in-Terms-of-Gromov-Ledouxs-Expansion-Coefficients-on/4846ojm.full

zbMATH Keywords

diameterdoubling metric measure spacesconcentration functionsGromov's and Ledoux's expansion coefficients

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Cites Work

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• Metric measure geometry. Gromov's theory of convergence and concentration of metrics and measures
• A remark on hypercontractivity and the concentration of measure phenomenon in a compact Riemannian manifold
• On the role of convexity in isoperimetry, spectral gap and concentration
• Unconditional and symmetric sets in \(n\)-dimensional normed spaces
• Eigenvalue comparison theorems and its geometric applications
• Differentiability of Lipschitz functions on metric measure spaces
• Lower bound estimates of the first eigenvalue for compact manifolds with positive Ricci curvature
• Levels of concentration between exponential and Gaussian
• Sobolev inequalities and Myers's diameter theorem for an abstract Markov generator
• A differentiable structure for metric measure spaces
• Quasisymmetric embeddings, the observable diameter, and expansion properties of graphs
• Riemannian manifolds with positive mean curvature
• Inégalités isopérimétriques et applications
• A Topological Application of the Isoperimetric Inequality
• Optimal Transport
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu

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