A fibered Tukia theorem for nilpotent Lie groups

2023/04/25 by Dymarz, Tullia, Fisher, David, Xie, Xiangdong
#30L10 22E25 20F65 #Complex Variables (math.CV) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2305.16149

Abstract

We establish a Tukia-type theorem for uniform quasiconformal groups of a Carnot group. More generally we establish a fiber bundle version (or foliated version) of Tukia theorem for uniform quasiconformal groups of a nilpotent Lie group whose Lie algebra admits a diagonalizable derivation with positive eigenvalues. These results have applications to quasi-isometric rigidity of solvable groups [DFX].

Related

• A Tukia-type theorem for nilpotent Lie groups and quasi-isometric rigidity of solvable groups
• On quasi-isometric nilpotent Lie groups
• Contact and 1-quasiconformal maps on Carnot groups
• Large scale geometry of certain solvable groups
• Metriques de Carnot-Caratheodory et Quasiisometries des Espaces Symetriques de rang un