# Sharp quantitative nonembeddability of the Heisenberg group into superreflexive Banach spaces

@article{Austin2010SharpQN,
title={Sharp quantitative nonembeddability of the Heisenberg group into superreflexive Banach spaces},
author={T. Austin and A. Naor and R. Tessera},
journal={arXiv: Metric Geometry},
year={2010}
}
• Published 2010
• Mathematics
• arXiv: Metric Geometry
• Let $\H$ denote the discrete Heisenberg group, equipped with a word metric $d_W$ associated to some finite symmetric generating set. We show that if $(X,\|\cdot\|)$ is a $p$-convex Banach space then for any Lipschitz function $f:\H\to X$ there exist $x,y\in \H$ with $d_W(x,y)$ arbitrarily large and $$\label{eq:comp abs} \frac{\|f(x)-f(y)\|}{d_W(x,y)}\lesssim \left(\frac{\log\log d_W(x,y)}{\log d_W(x,y)}\right)^{1/p}.$$ We also show that any embedding into $X$ of a… CONTINUE READING
24 Citations

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