Illinois Journal of Mathematics

Uniformity from Gromov hyperbolicity

David Herron, Nageswari Shanmugalingam, and Xiangdong Xie

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We show that in a metric space $X$ with annular convexity, uniform domains are precisely those Gromov hyperbolic domains whose quasiconformal structure on the Gromov boundary agrees with that on the boundary in $X$. As an application, we show that quasimöbius maps between geodesic spaces with annular convexity preserve uniform domains. These results are quantitative.

Article information

Illinois J. Math., Volume 52, Number 4 (2008), 1065-1109.

First available in Project Euclid: 18 November 2009

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Zentralblatt MATH identifier

Primary: 30C65: Quasiconformal mappings in $R^n$ , other generalizations 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces


Herron, David; Shanmugalingam, Nageswari; Xie, Xiangdong. Uniformity from Gromov hyperbolicity. Illinois J. Math. 52 (2008), no. 4, 1065--1109. doi:10.1215/ijm/1258554351.

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