Uniform Metric Graphs

We prove that every complete metric space “is” the boundary of a uniform length space whose quasihyperbolization is a geodesic visual Gromov hyperbolic space. There is a natural quasimöbius identification of the original space’s conformal gauge with the canonical gauge on the Gromov boundary. All pa...

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Bibliographic Details
Published in:The Journal of geometric analysis 2024-10, Vol.34 (10), Article 306
Main Author: Herron, David A.
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Global Analysis and Analysis on Manifolds
Hyperbolic coordinates
Mathematics
Mathematics and Statistics
Metric space
Parameter identification
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Summary:We prove that every complete metric space “is” the boundary of a uniform length space whose quasihyperbolization is a geodesic visual Gromov hyperbolic space. There is a natural quasimöbius identification of the original space’s conformal gauge with the canonical gauge on the Gromov boundary. All parameters are absolute constants.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-024-01735-1