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arXiv · 2506.07130

Combinatorial p-th Calabi flow for finite and infinite ideal circle patterns

Xiaorui Yang·Hao Yu
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Abstract

This paper presents a comprehensive study of the combinatorial $p$-th Calabi flow for both finite and infinite ideal circle patterns. In the finite case, we establish a sharp criterion: the combinatorial $p$-th Calabi flow with $p>1$ converges if and only if a constant curvature metric exists in the underlying geometric background. In the infinite setting, we prove the long-time existence of solutions to the combinatorial $p$-th Calabi flow for $p \geq 2$, representing a significant advance in the theory of curvature flows on infinite structures.

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Xiaorui Yang, Hao Yu. 2025-06-10. Combinatorial p-th Calabi flow for finite and infinite ideal circle patterns. https://arxiv.org/abs/2506.07130

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