发表机构
South China University of Technology; Nanjing University of Posts and Telecommunications; Tsinghua University（华南理工大学; 南京邮电大学; 清华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过共形四面体的对偶刻画和扩展变分原理，证明了常曲率空间中四面体及3-流形上球堆积的全局刚性，并推广至高维共形单形。
AI 中文摘要
本文研究了常曲率空间中共形四面体的对偶刻画，发展了一种几何技术，以获得四面体上双曲、欧氏、球面及理想双曲球堆积的全局刚性。此外，我们建立了扩展变分原理，以获得3-流形上（理想）双曲球堆积的全局刚性。我们还将共形四面体推广到更高维，并提供了常曲率空间中共形$n(\u22653)$-单形的刻画，这对研究高维球堆积具有实用价值。
英文摘要
In this paper, we give the dual characterization of conformal tetrahedra in constant curvature spaces, which develops a geometric technique to obtain the global rigidity of (ideal) hyperbolic, Euclidean, spherical sphere packings on a tetrahedron. Moreover, we introduce ideal hyperbolic sphere packings and extend the variational principle to obtain the global rigidity of (ideal) hyperbolic sphere packings on 3-manifolds. We also provide a characterization of conformal $n(\ge3)$-simplices in constant curvature spaces, which is useful for studying higher-dimensional sphere packings.
