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Conformal tetrahedra and global rigidity of sphere packings in constant curvature background geometry
Abstract
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(≥3)-simplices in constant curvature spaces, which is useful for studying higher-dimensional sphere packings.
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BibTeX
@misc{he2026conformal,
title = {{Conformal tetrahedra and global rigidity of sphere packings in constant curvature background geometry}},
author = {Zunwu He and Guangming Hu and Ziping Lei},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08856},
eprint = {2609.08856},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08856},
}
RIS
TY - UNPB
TI - Conformal tetrahedra and global rigidity of sphere packings in constant curvature background geometry
AU - Zunwu He
AU - Guangming Hu
AU - Ziping Lei
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.08856
UR - https://arxiv.org/abs/2609.08856
AB - 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(≥3)-simplices in constant curvature spaces, which is useful for studying higher-dimensional sphere packings.
ER -