Invertible Carnot Groups
David M. Freeman

TL;DR
This paper characterizes specific Carnot groups that admit a 1-quasiconformal metric inversion, linking their structure to Lie groups of Heisenberg type satisfying the $J^2$-condition, and extends the concept to certain non-fractal metric spaces.
Contribution
It provides a complete characterization of Carnot groups with 1-quasiconformal inversions and extends the framework to non-fractal metric spaces.
Findings
Carnot groups with 1-quasiconformal metric inversion are Lie groups of Heisenberg type satisfying the $J^2$-condition
Characterization of inversion invariant bi-Lipschitz homogeneity for certain non-fractal metric spaces
Link between algebraic conditions and geometric inversion properties
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.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Analytic and geometric function theory
