No dimension reduction for doubling subsets of $\ell_q$ when $q>2$ revisited
Metric Geometry
2021-03-10 v1
Abstract
We revisit the main results from \cites{BGN_SoCG14,BGN_SIAM15} and \cite{LafforgueNaor14_GD} about the impossibility of dimension reduction for doubling subsets of for . We provide an alternative elementary proof of this impossibility result that combines the simplicity of the construction in \cites{BGN_SoCG14,BGN_SIAM15} with the generality of the approach in \cite{LafforgueNaor14_GD} (except for targets). One advantage of this different approach is that it can be naturally generalized to obtain embeddability obstructions into non-positively curved spaces or asymptotically uniformly convex Banach spaces.
Keywords
Cite
@article{arxiv.2103.05080,
title = {No dimension reduction for doubling subsets of $\ell_q$ when $q>2$ revisited},
author = {Florent P. Baudier and Krzysztof Swieçicki and Andrew Swift},
journal= {arXiv preprint arXiv:2103.05080},
year = {2021}
}
Comments
17 pages, 1 figure