Large scale geometry of negatively curved $\R^n \rtimes \R$.

Authors: Xiangdong Xie
Subjects: Group Theory
link: http://arxiv.org/abs/1001.0147
Abstract

We classify all negatively curved $\R^n \rtimes \R$ up to quasiisometry. We
show that all quasiisometries 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.