Rigidity of fiber-preserving quasisymmetric maps

2015/01/10 by Enrico Le Donne, Donne, Enrico Le, Xiangdong Xie +1
Mathematics · #22E25 #30L10 #53C17 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1501.02391

openalex publication_date 2015/01/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We show that fiber-preserving quasisymmetric maps are biLipschitz. As an application, we show that quasisymmetric maps on Carnot groups with reducible first stratum are biLipschitz.

Citations

• Quasiconformal maps in metric spaces with controlled geometry
• Metriques de Carnot-Caratheodory et Quasiisometries des Espaces Symetriques de rang un

Related

• Quasiconformal maps on non-rigid Carnot groups
• Quasisymmetric maps of boundaries of amenable hyperbolic groups
• Sobolev mappings between nonrigid Carnot groups
• Quasisymmetric rigidity of square Sierpinski carpets
• Pansu pullback and rigidity of mappings between Carnot groups