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

2012/11/14 by David, Guy, Snipes, Marie
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1211.3223

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∈ (1/2,1), we can find a bilipschitz mapping F = (E,d^α) → \R^N.

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