TITLE   : Assouad's Theorem with Dimension Independent of the Snowflaking

AUTHORS : Assaf Naor and Ofer Neiman

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