Complex Hyperbolic Elliptics Preserving Lagrangian Planes

Mengmeng Xu; Yibo Zhang

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arXiv · 2603.14470

Complex Hyperbolic Elliptics Preserving Lagrangian Planes

Mengmeng Xu·Yibo Zhang

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Abstract

For a regular, real elliptic isometry $f$ of finite order in $\mathbf{H}_{\mathbb{C}}^2$, we determine the explicit cellular structure of the Ford domain of $\langle f \rangle$ with respect to the extended Cygan metric, provided the centre of the Ford domain lies on the ideal boundary of a Lagrangian plane preserved by $f$. As an application, we give a sufficient condition for complex hyperbolic $(n,\infty,\infty)$-triangle groups to be discrete and faithful that is easy to verify.

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Mengmeng Xu, Yibo Zhang. 2026-03-15. Complex Hyperbolic Elliptics Preserving Lagrangian Planes. https://arxiv.org/abs/2603.14470

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