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<p>The geometric structure of three-dimensional manifolds is a fundamental problem in geometric topology. In this paper, we investigate the ideal circle pattern problem on a surface with boundaries under a cellular decomposition. Employing the variational method, we establish a series of equivalent conditions for the existence of a circle pattern in both Euclidean and hyperbolic background geometries.</p>

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The Ideal Circle Pattern with Boundaries via Analytic Method

  • 期刊论文

  • 发表日期：

    2025年5月5日

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  • Hao Yu

摘要

The geometric structure of three-dimensional manifolds is a fundamental problem in geometric topology. In this paper, we investigate the ideal circle pattern problem on a surface with boundaries under a cellular decomposition. Employing the variational method, we establish a series of equivalent conditions for the existence of a circle pattern in both Euclidean and hyperbolic background geometries.