Invertible Carnot Groups

David M. Freeman

Analysis and Geometry in Metric Spaces (2014)

  • Volume: 2, Issue: 1, page 248-257, electronic only
  • ISSN: 2299-3274

Abstract

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We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the J2-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity. A more general characterization of inversion invariant bi-Lipschitz homogeneity for certain non-fractal metric spaces is also provided.

How to cite

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David M. Freeman. "Invertible Carnot Groups." Analysis and Geometry in Metric Spaces 2.1 (2014): 248-257, electronic only. <http://eudml.org/doc/267299>.

@article{DavidM2014,
abstract = {We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the J2-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity. A more general characterization of inversion invariant bi-Lipschitz homogeneity for certain non-fractal metric spaces is also provided.},
author = {David M. Freeman},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {metric inversion; bi-Lipschitz homogeneity; Carnot groups; sub-Riemannian geometry},
language = {eng},
number = {1},
pages = {248-257, electronic only},
title = {Invertible Carnot Groups},
url = {http://eudml.org/doc/267299},
volume = {2},
year = {2014},
}

TY - JOUR
AU - David M. Freeman
TI - Invertible Carnot Groups
JO - Analysis and Geometry in Metric Spaces
PY - 2014
VL - 2
IS - 1
SP - 248
EP - 257, electronic only
AB - We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the J2-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity. A more general characterization of inversion invariant bi-Lipschitz homogeneity for certain non-fractal metric spaces is also provided.
LA - eng
KW - metric inversion; bi-Lipschitz homogeneity; Carnot groups; sub-Riemannian geometry
UR - http://eudml.org/doc/267299
ER -

References

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