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arXiv · 2201.03105

Some remarks on the Gehring-Hayman theorem

Sari Rogovin·Hyogo Shibahara·Qingshan Zhou
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Abstract

In this paper we provide new characterizations of the Gehring-Hayman theorem from the point of view of Gromov boundary and uniformity. We also determine the critical exponents for the uniformized space to be a uniform space in the case of the hyperbolic spaces, the model spaces $\mathbb{M}^{\kappa}_n$ of the sectional curvature $\kappa<0$ with the dimension $n \geq 2$ and hyperbolic fillings.

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Sari Rogovin, Hyogo Shibahara, Qingshan Zhou. 2022-01-09. Some remarks on the Gehring-Hayman theorem. https://arxiv.org/abs/2201.03105

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