Markov convexity and local rigidity of distorted metrics

DOI10.4171/JEMS/362zbMath1266.46016OpenAlexW2054974227MaRDI QIDQ1932211

Assaf Naor, Manor Mendel

Publication date: 17 January 2013

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jems/362

zbMATH Keywords

uniformly convex Banach spaceHamming cubebilipschitz embeddingsLipschitz quotienttree metricMarkov convexity

Mathematics Subject Classification ID

Local theory of Banach spaces (46B07) Probabilistic methods in Banach space theory (46B09) Distance in graphs (05C12) Nonlinear classification of Banach spaces; nonlinear quotients (46B80) Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85) Geometric embeddings of metric spaces (30L05)

Related Items (22)

Metric Characterizations of Some Classes of Banach Spaces ⋮ Nonexistence of embeddings with uniformly bounded distortions of Laakso graphs into diamond graphs ⋮ Vertical perimeter versus horizontal perimeter ⋮ METRIC INEQUALITIES ⋮ Metric Embedding via Shortest Path Decompositions ⋮ Estimates on the Markov convexity of Carnot groups and quantitative nonembeddability ⋮ Umbel convexity and the geometry of trees ⋮ Metric characterizations of superreflexivity in terms of word hyperbolic groups and finite graphs ⋮ Spectral calculus and Lipschitz extension for barycentric metric spaces ⋮ Markov convexity and nonembeddability of the Heisenberg group ⋮ Coarse differentiation and quantitative nonembeddability for Carnot groups ⋮ Heat flow and quantitative differentiation ⋮ Yet another short proof of Bourgain's distortion estimate for embedding of trees into uniformly convex Banach spaces ⋮ Snowflake universality of Wasserstein spaces ⋮ The transfer of property $(\beta )$ of Rolewicz by a uniform quotient map ⋮ (β)-distortion of some infinite graphs ⋮ Impossibility of dimension reduction in the nuclear norm ⋮ An average John theorem ⋮ Quantitative affine approximation for UMD targets ⋮ A characterization of superreflexivity through embeddings of lamplighter groups ⋮ Thick families of geodesics and differentiation ⋮ Metric spaces nonembeddable into Banach spaces with the Radon–Nikodým property and thick families of geodesics

Cites Work

• Unnamed Item
• Markov chains, Riesz transforms and Lipschitz maps
• Sharp uniform convexity and smoothness inequalities for trace norms
• Affine approximation of Lipschitz functions and nonlinear quotients

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