Rigidity of infinite inversive distance circle packings in the plane

Yanwen Luo; Xu Xu; Siqi Zhang

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arXiv · 2211.07464

Rigidity of infinite inversive distance circle packings in the plane

Yanwen Luo·Xu Xu·Siqi Zhang

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Abstract

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.

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Yanwen Luo, Xu Xu, Siqi Zhang. 2022-11-14. Rigidity of infinite inversive distance circle packings in the plane. https://arxiv.org/abs/2211.07464

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