Vol. 265, No. 1, 2013

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Quasisymmetric homeomorphisms on reducible Carnot groups

Xiangdong Xie

Vol. 265 (2013), No. 1, 113–122
Abstract

We show that quasisymmetric homeomorphisms between (most) reducible Carnot groups are bilipschitz. This implies rigidity for quasi-isometries between certain negatively curved homogeneous manifolds. The proof uses Pansu’s differentiability theorem for quasisymmetric homeomorphisms between Carnot groups.

Keywords
quasisymmetric homeomorphism, Carnot groups, Pansu differentiability
Mathematical Subject Classification 2010
Primary: 53C17, 53C23, 30L10
Milestones
Received: 17 May 2012
Revised: 5 May 2013
Accepted: 7 June 2013
Published: 28 August 2013
Authors
Xiangdong Xie
Department of Mathematics and Statistics
Bowling Green State University
Bowling Green, OH 43403
United States