Uniformity from Gromov hyperbolicity
David Herron, Nageswari Shanmugalingam, and Xiangdong Xie
Source: Illinois J. Math. Volume 52, Number 4
(2008), 1065-1109.
Abstract
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.
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Permanent link to this document: http://projecteuclid.org/euclid.ijm/1258554351
Zentralblatt MATH identifier: 05660647
Mathematical Reviews number (MathSciNet): MR2595756
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