Some applications of ball's extension theorem

Manor Mendel, Assaf Naor

Research output: Contribution to journalArticlepeer-review


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
Issue number9
StatePublished - Sep 2006


  • Bi-Lipschitz embeddings
  • Lipschitz extension

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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