A Tukia-type theorem for nilpotent Lie groups and quasi-isometric rigidity of solvable groups

2023/04/24 by Dymarz, Tullia, Fisher, David, Xie, Xiangdong
#20F16 #20F65 #30L10 #Complex Variables (math.CV) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2304.12498

Abstract

In this paper we study uniform quasiconformal groups of Carnot-by-Carnot groups. We show that they can be conjugated into conformal groups provided the induced action on the space of distinct pairs is cocompact. Following the approach of Eskin-Fisher-Whyte these results have applications to quasi-isometric rigidity of certain solvable groups.

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