Quasiconformal mappings in the hyperbolic Heisenberg group and a lifting theorem

2019/09/26 by Platis, Ioannis D.
#30C60 #30C75 #30L10 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.11955

Abstract

A study of smooth contact quasiconformal mappings of the hyperbolic Heisenberg group is presented in this paper. Our main result is a Lifting Theorem; according to this, a symplectic quasiconformal mapping of the hyperbolic plane can be lifted to a circles preserving quasiconformal mapping of the hyperbolic Heisenberg group.

Related

• Geometric construction of quasiconformal mappings in the Heisenberg group
• Hardy spaces and quasiconformal maps in the Heisenberg group
• Contact lifts and Holder lifts to central extension of Carnot groups
• Global contact and quasiconformal mappings of Carnot groups
• A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group