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Abstract
Möbius invariants of general circle packings are defined in terms of cross ratios. The necessary and sufficient conditions of existence of circle packings are established by the techniques of Möbius invariants. It is shown that circle packings are uniquely determined, up to Möbius transformations, by their Möbius invariants. The rigidity of infinite circle packings with bounded degree is proved using the approach of Möbius invariants.
Acknowledgements
The authors would like to thank the anonymous referees’ valuable comments and suggestions to improve the paper.
Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
This project is supported in part NSF of China [11161004] and NSF of Guangxi [2013GXNSFAA019015].