On the deformation of inversive distance circle packings, II

Abstract

We show that the results in \cite{Ge-Jiang1} 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.

Comments are welcome

References in corpus (4)

• Rigidity of Polyhedral Surfaces
• Geometric triangulations and discrete Laplacians on manifolds
• $\alpha$-curvatures and $\alpha$-flows on low dimensional triangulated manifolds
• Volume and rigidity of hyperbolic polyhedral $3$-manifolds

Cited by in corpus (14)

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• On the deformation of ball packings
• A new proof of Bowers-Stephenson conjecture
• Rigidity of discrete conformal structures on surfaces
• Parameterized discrete uniformization theorems and curvature flows for polyhedral surfaces, I
• On the global rigidity of sphere packings on 3-dimensional manifolds
• Fractional combinatorial Calabi flow on surfaces
• Rigidity of inversive distance circle packings revisited
• On a combinatorial curvature for surfaces with inversive distance circle packing metrics
• Circle patterns on surfaces of finite topological type
• Combinatorial Ricci flow on cusped 3-manifolds
• Tame the flexibility of circle patterns
• Combinatorial Calabi flow with surgery on surfaces
• Conformal Mesh Parameterization Using Discrete Calabi Flow