Abstract
We present two applications of Ball's extension theorem. First we observe that Ball's extension theorem, together with the recent solution of Ball's Markov type 2 problem due to Naor, Peres, Schramm and Sheffield, imply a generalization, and an alternative proof of, the Johnson-Lindenstrauss extension theorem. Second, we prove that the distortion required to embed the integer lattice {0,1,..., m} n, equipped with the ℓ p n metric, in any 2-uniformly convex Banach space is of order min {n 1/2-1/p, m 1-2/p}.
Original language | English (US) |
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Pages (from-to) | 2577-2584 |
Number of pages | 8 |
Journal | Proceedings of the American Mathematical Society |
Volume | 134 |
Issue number | 9 |
DOIs | |
State | Published - Sep 2006 |
Keywords
- Bi-Lipschitz embeddings
- Lipschitz extension
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics