Rough isometry between Gromov hyperbolic spaces and unbounded uniformization
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917007628173312 |
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| author | Allu, Vasudevarao Jose, Alan P |
| author_facet | Allu, Vasudevarao Jose, Alan P |
| contents | In a recent paper, Zhou, Ponnusamy, and Rasila [Math. Nachr. (2025)] have established that the conformal deformations, with parameter $ε>0$, of a Gromov hyperbolic space via Busemann functions are uniform spaces for sufficiently small $ε$. In this paper, we demonstrate that if two proper, roughly starlike Gromov hyperbolic spaces are roughly isometric, then the uniformity of their conformal deformations is a simultaneous property; that is, either both are uniform spaces or neither is. Our results provide a counterpart to the work of Shanmugalingam and Lindquist [Ann. Fenn. Math. (2021)]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11114 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rough isometry between Gromov hyperbolic spaces and unbounded uniformization Allu, Vasudevarao Jose, Alan P Metric Geometry Complex Variables 53C23, 30L05 In a recent paper, Zhou, Ponnusamy, and Rasila [Math. Nachr. (2025)] have established that the conformal deformations, with parameter $ε>0$, of a Gromov hyperbolic space via Busemann functions are uniform spaces for sufficiently small $ε$. In this paper, we demonstrate that if two proper, roughly starlike Gromov hyperbolic spaces are roughly isometric, then the uniformity of their conformal deformations is a simultaneous property; that is, either both are uniform spaces or neither is. Our results provide a counterpart to the work of Shanmugalingam and Lindquist [Ann. Fenn. Math. (2021)]. |
| title | Rough isometry between Gromov hyperbolic spaces and unbounded uniformization |
| topic | Metric Geometry Complex Variables 53C23, 30L05 |
| url | https://arxiv.org/abs/2510.11114 |