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Transactions of the American Mathematical Society

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On the deformation of inversive distance circle packings, I


Authors: Huabin Ge and Wenshuai Jiang
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 52C26; Secondary 52C45, 53C15, 53C44
DOI: https://doi.org/10.1090/tran/7768
Published electronically: June 3, 2019
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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.


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Additional Information

Huabin Ge
Affiliation: School of Mathematics, Renmin University of China, Beijing 100872, People’s Republic of China
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
Email: jiangwenshuai@pku.edu.cn

DOI: https://doi.org/10.1090/tran/7768
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.
Article copyright: © Copyright 2019 American Mathematical Society