Large scale geometry of negatively curved ${\mathbb{R}}^n⋊\mathbb{R}$

Abstract

We classify all negatively curved ${\mathbb{R}}^n⋊\mathbb{R}$ 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.

Cited by in corpus (2)

• Quasiisometries of negatively curved homogeneous manifolds associated with Heisenberg groups
• On the logarithmic coarse structures of Lie groups and hyperbolic spaces