Nageswari Shanmugalingam, Xiangdong Xie
Published 2009-12-31Version 1
We show that for some negatively curved solvable Lie groups, all self quasiisometries are almost isometries. We prove this by showing that all self quasisymmetric maps of the ideal boundary (of the solvable Lie groups) are bilipschitz with respect to the visual metric. We also define parabolic visual metrics on the ideal boundary of Gromov hyperbolic spaces and relate them to visual metrics.
Quasisymmetric Maps on the Boundary of a Negatively Curved Solvable Lie Group
Large scale geometry of negatively curved $\R^n \rtimes \R$
An addendum to `A rigidity property for the set of all characters induced by valuations'
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