On the deformation of inversive distance circle packings, I
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Abstract:
In this paper, we consider Chow–Luo’s combinatorial Ricci flow in the inversive distance circle packing setting. Although a solution to the flow may develop singularities in finite time, we can always extend the solution so as it exists for all time and converges exponentially fast to a unique packing with prescribed cone angles. We also give partial results on the range of all attainable cone angles, which generalize the classical Andreev–Thurston theorem. This paper opens a program about the study of the deformations of discrete metrics and discrete curvatures.References
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Additional Information
- Huabin Ge
- Affiliation: School of Mathematics, Renmin University of China, Beijing 100872, People’s Republic of China
- MR Author ID: 955742
- Email: hbge@bjtu.edu.cn
- Wenshuai Jiang
- Affiliation: School of Mathematical Sciences, Zhejiang University, Zheda Road 38, Hangzhou, Zhejiang 310027, People’s Republic of China
- MR Author ID: 1170889
- Email: jiangwenshuai@pku.edu.cn
- Received by editor(s): February 16, 2018
- Received by editor(s) in revised form: November 20, 2018
- Published electronically: June 3, 2019
- Additional Notes: The first author was supported by NSFC no. 11871094.
The second author was supported by NSFC no. 11701507 and the Fundamental Research Funds for the Central Universities and the Engineering and Physical Sciences Research Council (EPSRC) on a Programme Grant entitled “Singularities of Geometric Partial Differential Equations,” reference no. EP/K00865X/1. - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 6231-6261
- MSC (2010): Primary 52C26; Secondary 52C45, 53C15, 53C44
- DOI: https://doi.org/10.1090/tran/7768
- MathSciNet review: 4024520