|Location:||MSRI: Simons Auditorium|
We show that quasiisometries between many negatively
curved solvable Lie groups are rigid: they preserve distance up to an
additive constant. This is equivalent to the statement that
quasisymmetric maps on the ideal boundary are biLipschitz.
The ideal boundary of these solvable Lie groups are nilpotent Lie groups with (nonstandard) homogeneous metrics.