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<p>This paper focuses on the generalized hyperbolic circle packings of finite polygonal cell decompositions with boundary values on surfaces with boundary. We investigate the problem of realizing generalized hyperbolic circle packings with given geodesic curvatures at bordered vertices and total geodesic curvatures at internal vertices and introduce the combinatorial <i>p</i>-th Calabi flows and the combinatorial fractional-order Calabi flows to find the desired generalized hyperbolic circle packings.</p>

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Combinatorial p-th Calabi Flows and Fractional-order Calabi Flows for Generalized Hyperbolic Circle Packings

  • 期刊论文

  • 发表日期：

    2026年6月5日

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  • Yu Sun,
  • Wenhao Fu,
  • Jiayang Chen,
  • Tao Liu

摘要

This paper focuses on the generalized hyperbolic circle packings of finite polygonal cell decompositions with boundary values on surfaces with boundary. We investigate the problem of realizing generalized hyperbolic circle packings with given geodesic curvatures at bordered vertices and total geodesic curvatures at internal vertices and introduce the combinatorial p-th Calabi flows and the combinatorial fractional-order Calabi flows to find the desired generalized hyperbolic circle packings.