Uniform spaces and Gromov hyperbolicity
by
Xiangdong Xie
University of Cincinnati
Coauthors: Nageswari Shanmugalingam, David Herron

We establish a connection between Gromov hyperbolic spaces and quasiconformal analysis: We characterize uniform spaces in terms of Gromov hyperbolic spaces and the quasiconformal structure on the Gromov boundary. We use a notion of inversions in general metric spaces. As an application, we show that a quasimobius map between domains in metric spaces with annulus quasiconvexity sends a uniform domain to a uniform domain.

Date received: February 23, 2006