Gromov hyperbolicity of the 𝑗̃_{𝐺} metric and boundary correspondence

Zhou, Qingshan; Ponnusamy, Saminathan; Guan, Tiantian

doi:10.1090/proc/15635

Gromov hyperbolicity of the $\tilde {j}_G$ metric and boundary correspondence
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by Qingshan Zhou, Saminathan Ponnusamy and Tiantian Guan PDF

Proc. Amer. Math. Soc. 150 (2022), 2839-2847 Request permission

Abstract:

Let $G\subsetneq \mathbb {R}^n$ be an open set. It is shown by Hästö that $G$ equipped with the $\tilde {j}_G$ metric is Gromov hyperbolic. The purpose of this paper is to show that there is a natural quasisymmetric correspondence between the Gromov boundary of $(G, \tilde {j}_G)$ and its Euclidean boundary $\partial G$. Both bounded and unbounded cases are in our considerations.

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