Some applications of ball's extension theorem

Manor Mendel, Assaf Naor

Research output: Contribution to journalArticle

16 Scopus citations

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 languageEnglish (US)
Pages (from-to)2577-2584
Number of pages8
JournalProceedings of the American Mathematical Society
Volume134
Issue number9
DOIs
StatePublished - Sep 2006

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Bi-Lipschitz embeddings
  • Lipschitz extension

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