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arXiv · 1211.3223

A constructive proof of the Assouad embedding theorem with bounds on the dimension

Guy David·Marie Snipes
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Abstract

We give a constructive proof of a theorem of Naor and Neiman, (to appear, Revista Matematica Iberoamercana), which asserts that if $(E,d)$ is a doubling metric space, there is an integer $N > 0$, that depends only on the metric doubling constant, such that for each exponent $α\in (1/2,1)$, we can find a bilipschitz mapping $F = (E,d^α) \to \R^N$.

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Guy David, Marie Snipes. 2012-11-14. A constructive proof of the Assouad embedding theorem with bounds on the dimension. https://arxiv.org/abs/1211.3223

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