Global rigidity of sphere packings in constant curvature background geometry

Zunwu He; Guangming Hu; Ziping Lei

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arXiv · 2609.08856

Global rigidity of sphere packings in constant curvature background geometry

Zunwu He·Guangming Hu·Ziping Lei

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Abstract

In this paper, we study the dual characterization of conformal tetrahedra in constant curvature spaces, which develops a geometric technique to obtain the global rigidity of hyperbolic, Euclidean, spherical and ideal hyperbolic sphere packings on a tetrahedron. Moreover, we establish the extended variational principle to obtain the global rigidity of the (ideal) hyperbolic sphere packings on 3-manifolds. We also generalize the conformal tetrahedra to higher dimensions and provide a characterization of conformal $n(\ge3)$-simplices in constant curvature spaces, which is useful for studying higher-dimensional sphere packings.

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Zunwu He, Guangming Hu, Ziping Lei. 2026-09-08. Global rigidity of sphere packings in constant curvature background geometry. https://arxiv.org/abs/2609.08856

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