Quasiisometries of negatively curved homogeneous manifolds associated with Heisenberg groups

Abstract

We study quasiisometries between negatively curved homogeneous manifolds associated with diagonalizable derivations on Heisenberg algebras. We classify these manifolds up to quasiisometry, and show that all quasiisometries between such manifolds (except when they are complex hyperbolic spaces) are almost similarities. We prove these results by studying the quasisymmetric maps on the ideal boundary of these manifolds.

References in corpus (2)

• Large scale geometry of negatively curved ${\mathbb{R}}^n⋊\mathbb{R}$
• Quasiconformal maps on non-rigid Carnot groups

Cited by in corpus (3)

• Rigidity of fiber-preserving quasisymmetric maps
• On quasi-isometry invariants associated to the derivation of a Heintze group
• Relative $L^p$-cohomology and Heintze groups