Infinite rigidity of inversive distance circle packings in the Poincar\'{e} disk
Differential Geometry
2025-11-14 v1
Abstract
The maximum principle for hyperbolic inversive distance circle packings on polyhedral surfaces is established,which unifies and generalizes existing maximum principles for various types of circle packings in the literature.As an application of this principle, a discrete Schwarz-Ahlfors lemma is established.Furthermore, an infinite rigidity theorem for weighted Delaunay triangulations of the Poincar\'{e} disk is proved,which generalizes He's hyperbolic rigidity result \cite{He2}.
Keywords
Cite
@article{arxiv.2511.09983,
title = {Infinite rigidity of inversive distance circle packings in the Poincar\'{e} disk},
author = {Yanwen Luo and Xu Xu and Chao Zheng},
journal= {arXiv preprint arXiv:2511.09983},
year = {2025}
}