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arXiv · 2411.00906

Uniformization of intrinsic Gromov hyperbolic spaces

Vasudevarao Allu·Alan P Jose
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Abstract

The purpose of this paper is to provide a uniformization procedure for Gromov hyperbolic spaces, which need not be geodesic or proper. We prove that the conformal deformation of a Gromov hyperbolic space is a bounded uniform space. Further, we show that there is a natural quasi-isometry between the Gromov boundary and the metric boundary of the deformed space. Our main results are a generalization of the results of Bonk, Heninonen, and Koskela [Proposition 4.5, Proposition 4.13, Ast\'{e}risque 270 (2001)].

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Vasudevarao Allu, Alan P Jose. 2024-11-01. Uniformization of intrinsic Gromov hyperbolic spaces. https://arxiv.org/abs/2411.00906

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