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arXiv · 1912.10439

Gromov hyperbolicity, John spaces and quasihyperbolic geodesics

Qingshan Zhou·Yaxiang Li·Antti Rasila
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Abstract

We show that every quasihyperbolic geodesic in a John space admitting a roughly starlike Gromov hyperbolic quasihyperbolization is a cone arc. This result provides a new approach to the elementary metric geometry question, formulated in \cite[Question 2]{Hei89}, which has been studied by Gehring, Hag, Martio and Heinonen. As an application, we obtain a simple geometric condition connecting uniformity of the space with the existence of Gromov hyperbolic quasihyperbolization.

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Qingshan Zhou, Yaxiang Li, Antti Rasila. 2019-12-22. Gromov hyperbolicity, John spaces and quasihyperbolic geodesics. https://arxiv.org/abs/1912.10439

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