Quasi-isometries between visual hyperbolic spaces

Mathematics – Geometric Topology

Scientific paper

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16 pages. In the new version, the property on the homeomorphism originally used to characterize quasi-isometry between the hyp

Scientific paper

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.

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