Geodesic
Metric cotype
Manor Mendel1 ; Assaf Naor2
1 Computer Science Division<br/>The Open University of Israel<br/>43107 Raanana<br/>Israel
2 Courant Institute of Mathematical Sciences<br/>New York University<br/>New York, NY 10012<br/>United States
Annals of mathematics, Tome 168 (2008) no. 1, pp. 247-298.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2008.168.247

Manor Mendel 1 ; Assaf Naor 2

1 Computer Science Division<br/>The Open University of Israel<br/>43107 Raanana<br/>Israel
2 Courant Institute of Mathematical Sciences<br/>New York University<br/>New York, NY 10012<br/>United States 
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Manor Mendel; Assaf Naor. Metric cotype. Annals of mathematics, Tome 168 (2008) no. 1, pp. 247-298. doi : 10.4007/annals.2008.168.247. http://geodesic.mathdoc.fr/articles/10.4007/annals.2008.168.247/

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