Geodesic
Some remarks on the Gehring–Hayman theorem
Sari Rogovin1 ; Hyogo Shibahara2 ; Qingshan Zhou3
1 Maunula Secondary School and Helsinki School of Mathematics
2 University of Cincinnati, Department of Mathematical Sciences
3 Foshan University, School of Mathematics and Big Data
Annales Fennici Mathematici, Tome 48 (2023) no. 1, pp. 141-152.

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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.
DOI : 10.54330/afm.125920
Keywords: Gromov hyperbolic space, uniform domain, uniform space, uniformization

Sari Rogovin 1 ; Hyogo Shibahara 2 ; Qingshan Zhou 3

1 Maunula Secondary School and Helsinki School of Mathematics
2 University of Cincinnati, Department of Mathematical Sciences
3 Foshan University, School of Mathematics and Big Data 
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Sari Rogovin; Hyogo Shibahara; Qingshan Zhou. Some remarks on the Gehring–Hayman theorem. Annales Fennici Mathematici, Tome 48 (2023) no. 1, pp. 141-152. doi : 10.54330/afm.125920. http://geodesic.mathdoc.fr/articles/10.54330/afm.125920/

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