Invertible Carnot Groups
Metric Geometry
2016-08-22 v2
Abstract
We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the -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.
Keywords
Cite
@article{arxiv.1408.4765,
title = {Invertible Carnot Groups},
author = {David M. Freeman},
journal= {arXiv preprint arXiv:1408.4765},
year = {2016}
}
Comments
10 pages. Revised version in which the proof of Theorem 1.1 is clarified