A Rigidity Property of Some Negatively Curved Solvable Lie Groups

Details A Rigidity Property of Some Negatively Curved Solvable Lie Groups A Rigidity Property of Some Negatively Curved Solvable Lie Groups

2009-12-31

arxiv.org/abs/1001.0150v1

Mathematics

Group Theory

Scientific paper

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.

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