Assouad's theorem with dimension independent of the snowflaking

Assaf Naor, Ofer Neiman

Research output: Contribution to journalArticle

16 Scopus citations

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 - Dec 1 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Assouad's theorem
  • Doubling metric spaces

Fingerprint Dive into the research topics of 'Assouad's theorem with dimension independent of the snowflaking'. Together they form a unique fingerprint.

  • Cite this