arXiv subjects

Alan P Jose

Publications and source records attributed to Alan P Jose.

4 recordsLinked to original sources

arXiv2025

Rough isometry between Gromov hyperbolic spaces and unbounded uniformization

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)].

math.MG↗

arXiv2024

Uniformization of intrinsic Gromov hyperbolic spaces with Busemann functions

For any intrinsic Gromov hyperbolic space we establish a Gehring-Hayman type theorem for conformally deformed spaces. As an application, we prove that any complete intrinsic hyperbolic space with atleast two points in the Gromov boundary can be uniformized by densities induced by Busemann functions. Furthermore, we establish that there exists a natural identification of the Gromov boundary of $X$ with the metric boundary of the deformed space.

math.CV↗

arXiv2024

Uniformization of intrinsic Gromov hyperbolic spaces

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)].

math.MG↗

arXiv2023

On invariance of John domains under quasisymmetric mappings

In this paper, we prove that if a homeomorphism is quasisymmetric relative to the boundary of the domain then it maps a length John domain to a diameter John domain. Moreover, we prove a necessary and sufficient condition for a diameter John domain to be length John and thereby prove that if $f:G\rightarrow G'$ is $(M, C)-$CQH map, where $G$ is a John domain, and the map extends to the boundary such that the extension is $η-$QS relative to $δG$ then $G'$ is a John domain. In addition, we characterize distance John domains using the weak minimizing property.

math.CV↗