Assouad's theorem with dimension independent of the snowflaking

Assaf Naor, Ofer Neiman

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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
Issue number4
StatePublished - 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Assouad's theorem
  • Doubling metric spaces


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