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<p>In this paper, we consider circle patterns with obtuse intersection angles via topological method. Inspired by Zhou’s work[<CitationRef CitationID="CR31">31</CitationRef>] on spherical case, we introduce some essential preliminaries which describe the “local rigidity” of circle pattern in hyperbolic background geometry and prove a series of results describing existence and rigidity of the circle patterns of certain types. Finally, we have also proposed a conjecture on Fuschsian polyhedron, which is hinted by our result.</p>

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Circle patterns with hyperbolic background via topological degree method

  • 期刊论文

  • 发表日期：

    2025年5月28日

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  • Huabin Ge,
  • Hao Yu

摘要

In this paper, we consider circle patterns with obtuse intersection angles via topological method. Inspired by Zhou’s work[31] on spherical case, we introduce some essential preliminaries which describe the “local rigidity” of circle pattern in hyperbolic background geometry and prove a series of results describing existence and rigidity of the circle patterns of certain types. Finally, we have also proposed a conjecture on Fuschsian polyhedron, which is hinted by our result.