On the deformation of inversive distance circle packings, I

Ge, Huabin; Jiang, Wenshuai

doi:10.1090/tran/7768

On the deformation of inversive distance circle packings, I
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Trans. Amer. Math. Soc. 372 (2019), 6231-6261 Request permission

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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