Large scale Sobolev inequalities on metric measure spaces and applications

DOI10.4171/RMI/557zbMath1194.53036arXivmath/0702751MaRDI QIDQ1001591

Romain Tessera

Publication date: 19 February 2009

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702751

zbMATH Keywords

isoperimetrySobolev inequalitiescoarse equivalencelarge-scale analysis on metric spacessymmetric random walks on groups

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Geometric group theory (20F65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) General properties and structure of locally compact groups (22D05)

Related Items (13)

Measure-scaling quasi-isometries ⋮ Quantitative measure equivalence between amenable groups ⋮ Harnack inequalities and Gaussian estimates for random walks on metric measure spaces ⋮ Geometric amenability in totally disconnected locally compact groups ⋮ Similarity problems, Følner sets and isometric representations of amenable semigroups ⋮ On the quantitative quasi-isometry problem: transport of Poincaré inequalities and different types of quasi-isometric distortion growth ⋮ Poincaré profiles of groups and spaces ⋮ Contracting automorphisms and \(L^p\)-cohomology in degree one ⋮ Quasi-isometrically embedded free sub-semigroups. ⋮ Isoperimetric inequalities, shapes of Følner sets and groups with Shalom's property \(H_{\mathrm{FD}}\) ⋮ On the vanishing of reduced 1-cohomology for Banach representations ⋮ Mean value property and harmonicity on Carnot-Carathéodory groups ⋮ Metabelian groups with large return probability

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