No dimension reduction for doubling subsets of lq when q > 2 revisited

[摘要] We revisit the main results from [6,7] and [23] about the impossibility of dimension reduction for doubling subsets of l(q) for q > 2. We provide an alternative elementary proof of this impossibility result that combines the simplicity of the construction in [6,7] with the generality of the approach in [23] (except for L-1 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. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-15

[关键词] Dimension reduction;Doubling spaces;Distortion of bi-Lipschitz embedddings;Laakso and diamond graphs;Asymptotic midpoint uniform convexity