Coarse differentiation and quantitative nonembeddability for Carnot groups

  title={Coarse differentiation and quantitative nonembeddability for Carnot groups},
  author={S. Li},
  journal={arXiv: Metric Geometry},
  • 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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