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<p>This paper constructs hyperbolic polyhedral metrics via circle packings. We introduce the curvature of circles as a parameter to include all three types of constant curvature curves in hyperbolic geometry. This provides a unified approach to producing polyhedral metrics for surfaces of more general topological types. The combinatorial total geodesic curvature serves as an effective tool for establishing the existence and uniqueness of the packing.</p>

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Circle packings and hyperbolic surfaces of finite type

  • 期刊论文

  • 发表日期：

    2025年9月22日

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  • Te Ba,
  • Guangming Hu,
  • Yu Sun

摘要

This paper constructs hyperbolic polyhedral metrics via circle packings. We introduce the curvature of circles as a parameter to include all three types of constant curvature curves in hyperbolic geometry. This provides a unified approach to producing polyhedral metrics for surfaces of more general topological types. The combinatorial total geodesic curvature serves as an effective tool for establishing the existence and uniqueness of the packing.