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PreprintCC BY 4.0arXiv

Thurston's sphere packing on 3-dimensional manifolds, II

  • Xiaokai He
  • Xu Xu
  • Chao Zheng
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Abstract

In this paper, we study the rigidity of Thurston's hyperbolic sphere packings on 3-dimensional manifolds. We prove that Thurston's hyperbolic sphere packing is locally determined by combinatorial scalar curvature. We further prove the infinitesimal rigidity that Thurston's hyperbolic sphere packing can not be deformed while keeping the combinatorial Ricci curvature fixed. The main tools include a characterization of the admissible space of Thurston's hyperbolic sphere packings, a variational formula for the dihedral angles of a tetrahedron and an identity for the variations of dihedral angles in a tetrahedron generated by Thurston's hyperbolic sphere packings.

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Cite

BibTeXRIS
BibTeX
@misc{he2026thurstons,
  title = {{Thurston's sphere packing on 3-dimensional manifolds, II}},
  author = {Xiaokai He and Xu Xu and Chao Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05232},
  eprint = {2610.05232},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05232},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Thurston's sphere packing on 3-dimensional manifolds, II
AU  - Xiaokai He
AU  - Xu Xu
AU  - Chao Zheng
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.05232
UR  - https://arxiv.org/abs/2610.05232
AB  - In this paper, we study the rigidity of Thurston's hyperbolic sphere packings on 3-dimensional manifolds. We prove that Thurston's hyperbolic sphere packing is locally determined by combinatorial scalar curvature. We further prove the infinitesimal rigidity that Thurston's hyperbolic sphere packing can not be deformed while keeping the combinatorial Ricci curvature fixed. The main tools include a characterization of the admissible space of Thurston's hyperbolic sphere packings, a variational formula for the dihedral angles of a tetrahedron and an identity for the variations of dihedral angles in a tetrahedron generated by Thurston's hyperbolic sphere packings.
ER  -