Some remarks on the Gehring–Hayman theorem

Authors

  • Sari Rogovin Maunula Secondary School and Helsinki School of Mathematics
  • Hyogo Shibahara University of Cincinnati, Department of Mathematical Sciences
  • Qingshan Zhou Foshan University, School of Mathematics and Big Data

DOI:

https://doi.org/10.54330/afm.125920

Keywords:

Gromov hyperbolic space, uniform domain, uniform space, uniformization

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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Published

2023-01-10

Issue

Vol. 48 No. 1 (2023)

Section

Articles

License

Copyright (c) 2022 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Rogovin, S., Shibahara, H., & Zhou, Q. (2023). Some remarks on the Gehring–Hayman theorem. Annales Fennici Mathematici, 48(1), 141-152. https://doi.org/10.54330/afm.125920