Assouad's theorem with dimension independent of the snowflaking
By Assaf Naor, Ofer Neiman. 2010
55 citations recorded by the source corpus.
It is shown that for every $K>0$ and $\e\in (0,1/2)$ there exist $N=N(K)\in \N$ and $D=D(K,\e)\in (1,\infty)$ with the following properties. For every separable metric space $(X,d)$ with doubling constant at most $K$, the metric space $(X,d^{1-\e})$ admits a bi-Lipschitz embedding into $\R^N$ with distortion at most $D$. The classical Assouad embedding theorem makes the same assertion, but with $N\to \infty$ as $\e\to 0$.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c95d787574083dcd80b2145cffbe9cec4bebd1f7
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- Assouad Dimension and Fractal Geometry (2020, background): “Naor and Neiman [215] proved that for ε ∈ (1/2, 1), one may choose the n in Theorem 13.”