Invertible Carnot Groups

Abstract

We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the $J^2$-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.

10 pages. Revised version in which the proof of Theorem 1.1 is clarified

References in corpus (2)

• Quasiconformal maps on non-rigid Carnot groups
• Quasiconformal maps on model Filiform groups