Assouad's theorem with dimension independent of the snowflaking

Assaf Naor, Ofer Neiman

Research output: Contribution to journalArticle

Abstract

It is shown that for every K > 0 and ε ∈ (0, 1/2) there exist N = N(K) ∈ N and D = D(K, ε) ∈ (1,∞) with the following properties. For every metric space (X, d) with doubling constant at most K, themetric space (X, d1-ε) admits a bi-Lipschitz embedding into RN with distortion at most D. The classical Assouad embedding theorem makes the same assertion, but with N →∞ as ε → 0.

Original languageEnglish (US)
Pages (from-to)1123-1142
Number of pages20
JournalRevista Matematica Iberoamericana
Volume28
Issue number4
DOIs
StatePublished - 2012

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Embedding Theorem
K-space
Doubling
Assertion
Metric space
Lipschitz
Theorem

Keywords

  • Assouad's theorem
  • Doubling metric spaces

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Assouad's theorem with dimension independent of the snowflaking. / Naor, Assaf; Neiman, Ofer.

In: Revista Matematica Iberoamericana, Vol. 28, No. 4, 2012, p. 1123-1142.

Research output: Contribution to journalArticle

Naor, Assaf ; Neiman, Ofer. / Assouad's theorem with dimension independent of the snowflaking. In: Revista Matematica Iberoamericana. 2012 ; Vol. 28, No. 4. pp. 1123-1142.
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