Spherical CR uniformizations of a sequence of hyperbolic 3-manifolds

Jiming Ma; Baohua Xie

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arXiv · 2608.11571

Spherical CR uniformizations of a sequence of hyperbolic 3-manifolds

Jiming Ma·Baohua Xie

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Abstract

Let $s782$ be the 2-cusped hyperbolic 3-manifold in the SnapPy census. Its spherical CR uniformization was established in \cite{JWX2023} using the Ford domain of the complex hyperbolic triangle group $\Delta_{4,4,\infty;\infty}$. By comparing the combinatorial structures of the Ford domain of $\Delta_{4,4,\infty;\infty}$ and the Dirichlet domain of $\Delta_{4,4,n;\infty}$, we prove that for each $n \geq 5$, the Dehn filling of $s782$ along the slope $(n-1)\mathcal{m}_1 + \mathcal{l}_1$ on its second cusp admits a spherical CR uniformization, where $(\mathcal{m}_1, \mathcal{l}_1)$ denotes the meridian-longitude system of a cusp in SnapPy notation.

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Jiming Ma, Baohua Xie. 2026-08-12. Spherical CR uniformizations of a sequence of hyperbolic 3-manifolds. https://arxiv.org/abs/2608.11571

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