Metric cotype

Manor Mendel, Assaf Naor

Research output: Contribution to journalArticle

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 L p coarsely or uniformly embeds into L q. 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
StatePublished - Jul 2008

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Metric Geometry
Banach space
Ramsey's Theorem
Metric
Theorem
Metric space
Open Problems
Analogue

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Mendel, M., & Naor, A. (2008). Metric cotype. Annals of Mathematics, 168(1), 247-298.

Metric cotype. / Mendel, Manor; Naor, Assaf.

In: Annals of Mathematics, Vol. 168, No. 1, 07.2008, p. 247-298.

Research output: Contribution to journalArticle

Mendel, M & Naor, A 2008, 'Metric cotype', Annals of Mathematics, vol. 168, no. 1, pp. 247-298.
Mendel M, Naor A. Metric cotype. Annals of Mathematics. 2008 Jul;168(1):247-298.
Mendel, Manor ; Naor, Assaf. / Metric cotype. In: Annals of Mathematics. 2008 ; Vol. 168, No. 1. pp. 247-298.
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