Gromov hyperbolicity and quasihyperbolic geodesics
Pekka Koskela, P\"aivi Lammi, Vesna Manojlovi\'c
TL;DR
This paper characterizes Gromov hyperbolicity of quasihyperbolic metric spaces using geometric properties of associated Ahlfors regular spaces, specifically the Gehring--Hayman and ball--separation conditions.
Contribution
It introduces new geometric criteria for Gromov hyperbolicity based on properties of the underlying length metric measure space.
Findings
Gromov hyperbolicity characterized by Gehring--Hayman condition
Gromov hyperbolicity characterized by ball--separation condition
Provides geometric criteria linking quasihyperbolic and Ahlfors regular spaces
Abstract
We characterize Gromov hyperbolicity of the quasihyperbolic metric space (\Omega,k) by geometric properties of the Ahlfors regular length metric measure space (\Omega,d,\mu). The characterizing properties are called the Gehring--Hayman condition and the ball--separation condition.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Analytic and geometric function theory · Geometric and Algebraic Topology