Quasi-isometries between visual hyperbolic spaces

2008/10/24 by Álvaro Martínez-Pérez, Martínez-Pérez, Álvaro · 1 citation
Mathematics · Medicine · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders

paper · pdf · doi:10.48550/arxiv.0810.4505

openalex publication_date 2008/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

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.

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• Quantitative correspondence between quasi-symmetric mappings on complete metric spaces and rough quasi-isometric mappings on their hyperbolic fillings

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