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Combinatorial Calabi Flows for Ideal Circle Patterns on Surfaces

Extending Ge-Hua-Zhou's combinatorial Ricci flows for ideal circle patterns to combinatorial Calabi flows in both Euclidean and hyperbolic background geometry. For any initial Euclidean (respectively hyperbolic) ideal circle pattern on a surface, the Calabi flow solution exists for all time and converges exponentially fast to a flat cone metric (respectively hyperbolic metric) (arXiv:2501.01605, math.DG/math.GT).

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Combinatorial Calabi flows with ideal circle patterns

In this paper, we extend the work of Ge-Hua-Zhou \cite{GHZ} on combinatorial Ricci flows for ideal circle patterns to combinatorial Calabi flows in both hyperbolic and Euclidean background geometry. …