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

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

2009-12-31

arxiv.org/abs/1001.0147v1

Mathematics

Group Theory

Scientific paper

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.

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