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) |
|---|---|
| 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 |
|---|---|
| Country/Territory | 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