# Coarse differentiation and quantitative nonembeddability for Carnot groups

@article{Li2013CoarseDA,
title={Coarse differentiation and quantitative nonembeddability for Carnot groups},
author={S. Li},
journal={arXiv: Metric Geometry},
year={2013}
}
• S. Li
• Published 2013
• Mathematics
• arXiv: Metric Geometry
• We give lower bound estimates for the macroscopic scale of coarse differentiability of Lipschitz maps from a Carnot group with the Carnot-Carath\'{e}odory metric $(G,\dcc)$ to a few different classes of metric spaces. Using this result, we derive lower bound estimates for quantitative nonembeddability of Lipschitz embeddings of $G$ into a metric space $(X,d_X)$ if $X$ is either an Alexandrov space with nonpositive or nonnegative curvature, a superreflexive Banach space, or another Carnot group… CONTINUE READING
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