Sobolev mappings between nonrigid Carnot groups

Bruce Kleiner, Xiangdong Xie, Stefan Müller

Publication date: 3 December 2021

Abstract: We consider mappings between Carnot groups. In this paper, which is a continuation of "Pansu pullback and rigidity of mappings between Carnot groups" (arXiv:2004.09271), we focus on Carnot groups which are nonrigid in the sense of Ottazzi-Warhurst. We show that quasisymmetric homeomorphisms are reducible in the sense that they preserve a special type of coset foliation, unless the group is isomorphic to R^n or a real or complex Heisenberg group (where the assertion fails). We use this to prove the quasisymmetric rigidity conjecture for such groups. The starting point of the proof is the pullback theorem established our previous paper.

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Sub-Riemannian geometry (53C17) Quasiconformal mappings in metric spaces (30L10)

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