Metric cotype

Manor Mendel, Assaf Naor

Research output: Contribution to conferencePaper

2 Scopus citations

Abstract

We introduce the notion of metric cotype, a property of metric spaces related to a property of normed spaces, called Rademacher cotype. Apart from settling a long standing open problem in metric geometry, this property is used to prove the following dichotomy: A family of metric spaces F is either almost universal (i.e., contains any finite metric space with any distortion > 1), or there exists α > 0, and arbitrarily large n-point metrics whose distortion when embedded in any member of F is at least Ω ((log n) α). The same property is also used to prove strong non-embeddability theorems of L q into L p, when q > max{2, p}. Finally we use metric cotype to obtain a new type of isoperimetric inequality on the discrete torus.

Original languageEnglish (US)
Pages79-88
Number of pages10
DOIs
StatePublished - Feb 28 2006
Externally publishedYes
EventSeventeenth Annual ACM-SIAM Symposium on Discrete Algorithms - Miami, FL, United States
Duration: Jan 22 2006Jan 24 2006

Other

OtherSeventeenth Annual ACM-SIAM Symposium on Discrete Algorithms
CountryUnited States
CityMiami, FL
Period1/22/061/24/06

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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    Mendel, M., & Naor, A. (2006). Metric cotype. 79-88. Paper presented at Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, Miami, FL, United States. https://doi.org/10.1145/1109557.1109567