Some applications of ball's extension theorem

Manor Mendel, Assaf Naor

Research output: Contribution to journalArticle

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

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Extension Theorem
Banach spaces
Ball
Johnson's theorem
Uniformly Convex Banach Space
Imply
Metric
Integer
Alternatives

Keywords

  • Bi-Lipschitz embeddings
  • Lipschitz extension

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Some applications of ball's extension theorem. / Mendel, Manor; Naor, Assaf.

In: Proceedings of the American Mathematical Society, Vol. 134, No. 9, 09.2006, p. 2577-2584.

Research output: Contribution to journalArticle

Mendel, Manor ; Naor, Assaf. / Some applications of ball's extension theorem. In: Proceedings of the American Mathematical Society. 2006 ; Vol. 134, No. 9. pp. 2577-2584.
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