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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Large scale geometry of negatively curved $\mathbb{R}^n \rtimes \mathbb{R}$

Xiangdong Xie

Geometry & Topology 18 (2014) 831–872
Abstract

We classify all negatively curved n up to quasi-isometry. We show that all quasi-isometries between such manifolds (except when they are bilipschitz to the real hyperbolic spaces) are almost similarities. We prove these results by studying the quasisymmetric maps on the ideal boundary of these manifolds.

Keywords
quasiisometry, quasisymmetric map, negatively curved solvable Lie groups
Mathematical Subject Classification 2010
Primary: 20F65, 30C65
Secondary: 53C20
References
Publication
Received: 20 July 2012
Revised: 5 May 2013
Accepted: 28 September 2013
Published: 20 March 2014
Proposed: Dmitri Burago
Seconded: Benson Farb, John Lott
Authors
Xiangdong Xie
Department of Mathematics and Statistics
Bowling Green State University
Bowling Green, OH 43403
USA
http://personal.bgsu.edu/~xiex/