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arXiv · 2309.02457

Rigidity of generalized Thurston's sphere packings on 3-dimensional manifolds with boundary

Xu Xu·Chao Zheng
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Abstract

Motivated by Guo-Luo's generalized circle packings on surfaces with boundary \cite{GL2}, we introduce the generalized Thurston's sphere packings on 3-dimensional manifolds with boundary. Then we investigate the rigidity of the generalized Thurston's sphere packings. We prove that the generalized Thurston's sphere packings are locally determined by the combinatorial scalar curvatures. We further prove the infinitesimal rigidity that the generalized Thurston's sphere packings can not be deformed while keeping the combinatorial Ricci curvatures fixed.

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Xu Xu, Chao Zheng. 2023-09-03. Rigidity of generalized Thurston's sphere packings on 3-dimensional manifolds with boundary. https://arxiv.org/abs/2309.02457

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