Gromov hyperbolicity, John spaces and quasihyperbolic geodesics
Complex Variables
2019-12-24 v1
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.
Keywords
Cite
@article{arxiv.1912.10439,
title = {Gromov hyperbolicity, John spaces and quasihyperbolic geodesics},
author = {Qingshan Zhou and Yaxiang Li and Antti Rasila},
journal= {arXiv preprint arXiv:1912.10439},
year = {2019}
}