Quasi-isometries between visual hyperbolic spaces
Geometric Topology
2008-11-14 v2
Abstract
We prove that a PQ-symmetric homeomorphism between two complete metric spaces can be extended to a quasi-isometry between their hyperbolic approximations. This result is used to prove that two visual Gromov hyperbolic spaces are quasi-isometric if and only if there is a PQ-symmetric homeomorphism between their boundaries.
Cite
@article{arxiv.0810.4505,
title = {Quasi-isometries between visual hyperbolic spaces},
author = {Álvaro Martínez-Pérez},
journal= {arXiv preprint arXiv:0810.4505},
year = {2008}
}
Comments
16 pages. In the new version, the property on the homeomorphism originally used to characterize quasi-isometry between the hyperbolic spaces is proved to be equivalent to being PQ-symmetric. Therefore, is no longer named as a new property and several changes are made following from this