Rigidity of infinite inversive distance circle packings in the plane
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866911076161945600 |
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| author | Luo, Yanwen Xu, Xu Zhang, Siqi |
| author_facet | Luo, Yanwen Xu, Xu Zhang, Siqi |
| contents | In 2004, Bowers-Stephenson [2] introduced the inversive distance circle packings as a natural generalization of Thurston's circle packings. They further conjectured the rigidity of infinite inversive distance circle packings in the plane. Motivated by the recent work of Luo-Sun-Wu [22] on Luo's vertex scaling, we prove Bower-Stephenson's conjecture for inversive distance circle packings in the hexagonal triangulated plane. This generalizes Rodin-Sullivan's famous result [13] on the rigidity of infinite tangential circle packings in the hexagonal triangulated plane. The key tools include a maximal principle for generic weighted Delaunay inversive distance circle packings and a ring lemma for the inversive distance circle packings in the hexagonal triangulated plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_07464 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rigidity of infinite inversive distance circle packings in the plane Luo, Yanwen Xu, Xu Zhang, Siqi Geometric Topology In 2004, Bowers-Stephenson [2] introduced the inversive distance circle packings as a natural generalization of Thurston's circle packings. They further conjectured the rigidity of infinite inversive distance circle packings in the plane. Motivated by the recent work of Luo-Sun-Wu [22] on Luo's vertex scaling, we prove Bower-Stephenson's conjecture for inversive distance circle packings in the hexagonal triangulated plane. This generalizes Rodin-Sullivan's famous result [13] on the rigidity of infinite tangential circle packings in the hexagonal triangulated plane. The key tools include a maximal principle for generic weighted Delaunay inversive distance circle packings and a ring lemma for the inversive distance circle packings in the hexagonal triangulated plane. |
| title | Rigidity of infinite inversive distance circle packings in the plane |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2211.07464 |