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arXiv · 2512.02829

Divergence-type semigroups in Kleinian groups and Hausdorff dimension

Inhyeok Choi
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Abstract

Let $\Gamma$ 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 $\Gamma$ is equal to the critical exponent of $\Gamma$. This gives a different proof of a theorem by M. Mj and W. Yang. Along the way, we construct subsemigroups of $\Gamma$ of divergence type and develop the Patterson--Sullivan theory.

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Inhyeok Choi. 2025-12-02. Divergence-type semigroups in Kleinian groups and Hausdorff dimension. https://arxiv.org/abs/2512.02829

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