On the deformation of inversive distance circle packings, III

Abstract We show that the results in [8] are still true in hyperbolic background geometry setting, that is, the solution to Chow–Luo's combinatorial Ricci flow can always be extended to a solution that exists for all time, furthermore, the extended solution converges exponentially fast if and only if there exists a metric with zero curvature. We also give some results about the range of discrete Gaussian curvatures, which generalize Andreev–Thurston's theorem to some extent.

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