Abstract
This paper focuses on the geometric properties of quasihyperbolic geodesics in centered John metric spaces. Our contribution is to provide a necessary and sufficient condition in centered John spaces such that quasihyperbolic geodesics terminating at the center to be cone arcs. As an application, we prove that for a centered John space which carries a Gromov hyperbolic quasihyperbolization, every quasihyperbolic geodesic terminating at the center is a cone arc.
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The authors are grateful for the constructive remarks of the referee.
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Qingshan Zhou was supported by NNSF of China (No. 11901090), by Guangdong Basic and Applied Basic Research Foundation (No. 2022A1515012441), by Department of Education of Guangdong Province, China (No. 2021KTSCX116), and Research Fund of Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology (No. 2020B1212030010).
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Zhou, Q., Ponnusamy, S. Quasihyperbolic Geodesics are Cone Arcs. J Geom Anal 34, 2 (2024). https://doi.org/10.1007/s12220-023-01448-x
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DOI: https://doi.org/10.1007/s12220-023-01448-x