### 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 language | English (US) |
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Title of host publication | Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms |

Pages | 79-88 |

Number of pages | 10 |

DOIs | |

State | Published - 2006 |

Event | Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms - Miami, FL, United States Duration: Jan 22 2006 → Jan 24 2006 |

### Other

Other | Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms |
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Country | United States |

City | Miami, FL |

Period | 1/22/06 → 1/24/06 |

### ASJC Scopus subject areas

- Software
- Discrete Mathematics and Combinatorics
- Safety, Risk, Reliability and Quality
- Chemical Health and Safety

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## Cite this

*Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 79-88) https://doi.org/10.1145/1109557.1109567