In this paper, we prove the global rigidity of sphere packings on 3-dimensional manifolds. This is a 3-dimensional analogue of the rigidity theorem of Andreev-Thurston and was conjectured by Cooper and Rivin. We also prove a global rigidity result using a combinatorial scalar curvature introduced by Ge and the author.

中文翻译：

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关于 $3$-维流形上球体填充的全局刚度

在本文中，我们证明了球体堆积在 3 维流形上的全局刚度。这是 Andreev-Thurston 刚性定理的 3 维模拟，由 Cooper 和 Rivin 推测。我们还使用 Ge 和作者引入的组合标量曲率证明了全局刚性结果。