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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    References

    SHOWING 1-10 OF 54 REFERENCES
    On the nonexistence of bilipschitz parameterizations and geometric problems about $A_\infty$-weights
    • 156
    Bi-Lipschitz Decomposition of Lipschitz functions into a Metric space
    • 16
    • Highly Influential
    • PDF
    Differentiating maps into L1, and the geometry of BV functions
    • 93
    • PDF
    Metric differentiation, monotonicity and maps to L1
    • 32
    • PDF
    Rectifiable metric spaces: local structure and regularity of the Hausdorff measure
    • 227
    • PDF
    On the rate of convergence to the asymptotic cone for nilpotent groups and subFinsler geometry
    • 36
    • Highly Influential
    • PDF
    Vertical versus horizontal Poincaré inequalities on the Heisenberg group
    • 17
    • Highly Influential
    • PDF
    Bourgain’s discretization Theorem
    • 21
    • PDF
    On the differentiability of Lispschitz maps from metric measure spaces to Banach spaces
    • 49
    • PDF