- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:47
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
28
2012
4
Assouad’s theorem with dimension independent of the snowflaking
Assaf
Naor
New York University, NEW YORK, UNITED STATES
Ofer
Neiman
Ben Gurion University of the Negev, BEER SHEVA, ISRAEL
Doubling metric spaces, Assouad’s theorem
It is shown that for every $K>0$ and $\varepsilon\in (0,1/2)$ there exist $N=N(K)\in \mathbb{N}$ and $D=D(K,\varepsilon)\in (1,\infty)$ with the following properties. For every metric space $(X,d)$ with doubling constant at most $K$, the metric space $(X,d^{1-\varepsilon})$ admits a bi-Lipschitz embedding into $\mathbb{R}^N$ with distortion at most $D$. The classical Assouad embedding theorem makes the same assertion, but with $N\to \infty$ as $\varepsilon\to 0$.
General
1123
1142
10.4171/RMI/706
http://www.ems-ph.org/doi/10.4171/RMI/706