Benoist-Hulin groups

Hideki Miyachi; Yannian Zhao

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arXiv · 2507.19927

Benoist-Hulin groups

Hideki Miyachi·Yannian Zhao

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Abstract

A Benoist-Hulin group is, by definition, a subgroup $\Gamma$ of ${\rm PSL}_2(\mathbb{C})$ such that any $\Gamma$-invariant closed set consisting of Jordan curves in the space of closed subsets of the Riemann sphere that are not singletons is composed of $K$-quasicircles for some $K \ge 1$. Y.Benoist and D.Hulin showed that the full group ${\rm PSL}_2(\mathbb{C})$ is a Benoist-Hulin group. In this paper, we develop the theory of Benoist-Hulin groups and show that both uniform lattices and parabolic subgroups are Benoist-Hulin groups.

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BibTeX RIS

Hideki Miyachi, Yannian Zhao. 2025-07-26. Benoist-Hulin groups. https://arxiv.org/abs/2507.19927

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