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<p>We study the combinatorial Calabi flow for ideal circle patterns in both hyperbolic and Euclidean background geometry. We prove that the flow exists for all time and converges exponentially fast to an ideal circle pattern metric on surfaces with prescribed attainable curvatures. As a consequence, we provide an algorithm to find the desired ideal circle patterns.</p>

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Combinatorial Calabi Flow for Ideal Circle Pattern

  • 期刊论文

  • 发表日期：

    2025年3月27日

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  • Shengyu Li,
  • Zhigang Wang

摘要

We study the combinatorial Calabi flow for ideal circle patterns in both hyperbolic and Euclidean background geometry. We prove that the flow exists for all time and converges exponentially fast to an ideal circle pattern metric on surfaces with prescribed attainable curvatures. As a consequence, we provide an algorithm to find the desired ideal circle patterns.