Benoist-Hulin groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911078546407424 |
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| author | Miyachi, Hideki Zhao, Yannian |
| author_facet | Miyachi, Hideki Zhao, Yannian |
| contents | A Benoist-Hulin group is, by definition, a subgroup $Γ$ of ${\rm PSL}_2(\mathbb{C})$ such that any $Γ$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19927 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Benoist-Hulin groups Miyachi, Hideki Zhao, Yannian Group Theory Complex Variables Dynamical Systems Geometric Topology Primary 30C62, Secondary 57M60 A Benoist-Hulin group is, by definition, a subgroup $Γ$ of ${\rm PSL}_2(\mathbb{C})$ such that any $Γ$-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. |
| title | Benoist-Hulin groups |
| topic | Group Theory Complex Variables Dynamical Systems Geometric Topology Primary 30C62, Secondary 57M60 |
| url | https://arxiv.org/abs/2507.19927 |