Geometric Analysis and Topology Seminar

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Large Scale Geometry of Negatively Curved Homogeneous Spaces

Speaker: Xiangdong Xie

Location: Warren Weaver Hall 202

Date: Friday, November 6, 2009, 11 a.m.

Synopsis:

We study quasi-isometries of a class of negatively curved homogeneous spaces. We show that every self quasi-isometry of such a homogeneous space is an almost isometry, that is, they preserve the distance up to an additive constant. We prove this by showing that every quasisymmetry of the ideal boundary is a bilipschitz homeomorphism (with respect to the visual metric on the ideal boundary).