Sphericalization with its applications in Gromov hyperbolic spaces
Metric Geometry
2020-09-30 v1 Complex Variables
Abstract
In this paper, we study certain applications of sphericalization in Gromov hyperbolic metric spaces. We first show that the doubling property regarding two classes of metrics on the Gromov boundary of hyperbolic spaces are coincided. Next, we obtain a characterization of unbounded Gromov hyperbolic domains via metric spaces sphericalization. Finally, we investigate the topological equivalence of Gromov hyperbolic -uniform domains between the Gromov boundary and the inner metric boundary.
Keywords
Cite
@article{arxiv.2009.13706,
title = {Sphericalization with its applications in Gromov hyperbolic spaces},
author = {Qingshan Zhou and Yaxiang Li and Xining Li},
journal= {arXiv preprint arXiv:2009.13706},
year = {2020}
}