Rigidity of inversive distance circle packings revisited

Xu Xu Wuhan University

Geometric Analysis and Geometric Topology Convex and Discrete Geometry mathscidoc:2104.15003

Advances in Mathematics, 332, 476–509, 2018.5
Inversive distance circle packing metric was introduced by P Bowers and K Stephenson as a generalization of Thurston’s circle packing metric. They conjectured that the inversive distance circle packings are rigid. For nonnegative inversive distance, Guo proved the infinitesimal rigidity and then Luo proved the global rigidity. In this paper, based on an observation of Zhou, we prove this conjecture for inversive distance in (−1, +∞)by variational principles. We also study the global rigidity of a combinatorial curvature with respect to the inversive distance circle packing metrics where the inversive distance is in (−1, +∞).
Inversive distance, Circle packing, Rigidity, Combinatorial curvature
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@inproceedings{xu2018rigidity,
  title={Rigidity of inversive distance circle packings revisited},
  author={Xu Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210405174441262991779},
  booktitle={Advances in Mathematics},
  volume={332},
  pages={476–509},
  year={2018},
}
Xu Xu. Rigidity of inversive distance circle packings revisited. 2018. Vol. 332. In Advances in Mathematics. pp.476–509. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210405174441262991779.
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