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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.02829 |
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| _version_ | 1866909942837936128 |
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| author | Choi, Inhyeok |
| author_facet | Choi, Inhyeok |
| contents | Let $Γ$ be a non-elementary, non-convex-cocompact Kleinian group acting on $\mathbb{H}^{d}$. We show that the Hausdorff dimension of the sublinearly conical Myrberg limit set of $Γ$ is equal to the critical exponent of $Γ$. This gives a different proof of a theorem by M. Mj and W. Yang. Along the way, we construct subsemigroups of $Γ$ of divergence type and develop the Patterson--Sullivan theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02829 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Divergence-type semigroups in Kleinian groups and Hausdorff dimension Choi, Inhyeok Dynamical Systems Group Theory Let $Γ$ be a non-elementary, non-convex-cocompact Kleinian group acting on $\mathbb{H}^{d}$. We show that the Hausdorff dimension of the sublinearly conical Myrberg limit set of $Γ$ is equal to the critical exponent of $Γ$. This gives a different proof of a theorem by M. Mj and W. Yang. Along the way, we construct subsemigroups of $Γ$ of divergence type and develop the Patterson--Sullivan theory. |
| title | Divergence-type semigroups in Kleinian groups and Hausdorff dimension |
| topic | Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2512.02829 |