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Metric cotype (2005)
| Content Provider | CiteSeerX |
|---|---|
| Author | Naor, Assaf Mendel, Manor |
| 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 Matouˇsek. |
| File Format | |
| Publisher Date | 2005-01-01 |
| Access Restriction | Open |
| Subject Keyword | Long Standing Open Problem Metric Ramsey Theorem Concrete Version Rademacher Cotype Ribe Theorem Nonlinear Theory Several Problem Quantitative Bound Maurey-pisier Theorem Banach Space Lov Sz Metric Space Nonlinear Analog Matou Sek Metric Geometry Classical Notion Metric Cotype Coarse Embeddings Uniformly Embeds |
| Content Type | Text |
