Rough isometry between Gromov hyperbolic spaces and unbounded uniformization
Metric Geometry
2025-10-14 v1 Complex Variables
Abstract
In a recent paper, Zhou, Ponnusamy, and Rasila [Math. Nachr. (2025)] have established that the conformal deformations, with parameter , of a Gromov hyperbolic space via Busemann functions are uniform spaces for sufficiently small . 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)].
Cite
@article{arxiv.2510.11114,
title = {Rough isometry between Gromov hyperbolic spaces and unbounded uniformization},
author = {Vasudevarao Allu and Alan P Jose},
journal= {arXiv preprint arXiv:2510.11114},
year = {2025}
}