Metric cotype

Manor Mendel, Assaf Naor

Research output: Contribution to journalArticle

53 Scopus citations

Abstract

We introduce the notion of cotype of a metric space, and prove that for Banach spaces it coincides with the classical notion of Rademacher cotype. This yields a concrete version of Ribe's theorem, settling a long standing open problem in the nonlinear theory of Banach spaces. We apply our results to several problems in metric geometry. Namely, we use metric cotype in the study of uniform and coarse embeddings, settling in particular the problem of classifying when Lp coarsely or uniformly embeds into Lq. We also prove a nonlinear analog of the Maurey-Pisier theorem, and use it to answer a question posed by Arora, Lovász, Newman, Rabani, Rabinovich and Vempala, and to obtain quantitative bounds in a metric Ramsey theorem due to Matoušek.

Original languageEnglish (US)
Pages (from-to)247-298
Number of pages52
JournalAnnals of Mathematics
Volume168
Issue number1
DOIs
StatePublished - Jul 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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