Uniformization of intrinsic Gromov hyperbolic spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915002567360512 |
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| author | Allu, Vasudevarao Jose, Alan P |
| author_facet | Allu, Vasudevarao Jose, Alan P |
| contents | 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, Astérisque 270 (2001)]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00906 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniformization of intrinsic Gromov hyperbolic spaces Allu, Vasudevarao Jose, Alan P Metric Geometry Complex Variables Primary 30C65, 30F45, Secondary 30C20 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, Astérisque 270 (2001)]. |
| title | Uniformization of intrinsic Gromov hyperbolic spaces |
| topic | Metric Geometry Complex Variables Primary 30C65, 30F45, Secondary 30C20 |
| url | https://arxiv.org/abs/2411.00906 |