Quasi-isometries between visual hyperbolic spaces
Abstract
Description
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.
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
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