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arXiv · 1704.07193

Quasihyperbolic geodesics are hyperbolic quasi-geodesics

David A Herron·Stephen M Buckley
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Abstract

This is a tale describing the large scale geometry of Euclidean plane domains with their hyperbolic or quasihyperbolic distances. We prove that in any hyperbolic plane domain, hyperbolic and quasihyperbolic quasi-geodesics are the same curves. We also demonstrate the simultaneous Gromov hyperbolicity of such domains with their hyperbolic or quasihyperbolic distances.

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David A Herron, Stephen M Buckley. 2017-04-24. Quasihyperbolic geodesics are hyperbolic quasi-geodesics. https://arxiv.org/abs/1704.07193

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