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<p>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 [Prop.&#xa0;4.5, Prop.&#xa0;4.13, Astérisque 270 (2001)].</p>

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Uniformization of Intrinsic Gromov Hyperbolic Spaces

  • 期刊论文

  • 发表日期：

    2026年5月21日

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  • Vasudevarao Allu,
  • Alan P. Jose

摘要

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 [Prop. 4.5, Prop. 4.13, Astérisque 270 (2001)].