Invertible Carnot Groups

2014/08/20 by David Freeman, Freeman, David M.
Mathematics · #30L05 #30L10 #53C17 #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1408.4765

openalex publication_date 2014/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Quasiconformal maps on non-rigid Carnot groups
• Quasisymmetric parametrizations of two-dimensional metric spheres
• Quasiconformal maps in metric spaces with controlled geometry

Related

• Metric Lie Groups. Carnot-Carathéodory spaces from the homogeneous viewpoint
• Quasiconformal maps on non-rigid Carnot groups
• A primer on Carnot groups: homogenous groups, CC spaces, and regularity of their isometries
• A metric boundary theory for Carnot groups
• A metric characterization of Carnot groups