Quantitative property A, Poincaré inequalities, \(L^p\)-compression and \(L^p\)-distortion for metric measure spaces

DOI10.1007/s10711-008-9286-5zbMath1162.46043arXivmath/0702384OpenAlexW2152570014MaRDI QIDQ960055

Romain Tessera

Publication date: 16 December 2008

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702384

zbMATH Keywords

Poincaré inequalitiescoarse embeddingproperty AHilbert compressionHilbert distortionuniform embeddings of metric spaces into Banach spaces

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Distance in graphs (05C12) Continuous and differentiable maps in nonlinear functional analysis (46T20)

Related Items (7)

Vertical perimeter versus horizontal perimeter ⋮ On the \(L^p\)-distortion of finite quotients of amenable groups ⋮ Stochastic approximation of lamplighter metrics ⋮ Compression bounds for Lipschitz maps from the Heisenberg group to \(L_{1}\) ⋮ Umbel convexity and the geometry of trees ⋮ Amenable groups with very poor compression into Lebesgue spaces ⋮ Vertical versus horizontal Poincaré inequalities on the Heisenberg group

Cites Work

• Asymptotic isoperimetry on groups and uniform embeddings into Banach spaces
• Metrics on diagram groups and uniform embeddings in a Hilbert space.
• The metrical interpretation of superreflexivity in Banach spaces
• Discrete groups, expanding graphs and invariant measures. Appendix by Jonathan D. Rogawski
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• Ahlfors \(Q\)-regular spaces with arbitrary \(Q>1\) admitting weak Poincaré inequality
• Warped cones and property A
• Quasi-isometrically embedded free sub-semigroups.
• Remarks on Yu’s ‘property A’ for discrete metric spaces and groups
• Girth and euclidean distortion
• Plongements lipschitziens dans ${\bbfR}\sp n$
• PLANE WITH $A_{\infty}$ -WEIGHTED METRIC NOT BILIPSCHITZ EMBEDDABLE TO ${\bb R}^n$
• EXACTNESS AND UNIFORM EMBEDDABILITY OF DISCRETE GROUPS

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