Sobolev mappings between nonrigid Carnot groups

Autor:	Kleiner, Bruce, Muller, Stefan, Xie, Xiangdong
Rok vydání:	2021
Předmět:	Mathematics - Differential Geometry 30C65 (Primary) 30L10 53C17 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: The contents of this paper originally appeared as the latter part of the arXiv preprint "Pansu pullback and rigidity of mappings between Carnot groups'' (arXiv:2004.09271)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2112.01866 Zobrazit plný text záznamu View this record from Arxiv