Rigidity of infinite inversive distance circle packings in the plane
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.
Keywords
Cite
@article{arxiv.2211.07464,
title = {Rigidity of infinite inversive distance circle packings in the plane},
author = {Yanwen Luo and Xu Xu and Siqi Zhang},
journal= {arXiv preprint arXiv:2211.07464},
year = {2025}
}
Comments
23 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:2204.08145