Generalized circle patterns on surfaces with cusps
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913790781554688 |
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| author | Xiong, Zhiwen Xu, Xu |
| author_facet | Xiong, Zhiwen Xu, Xu |
| contents | Guo and Luo introduced generalized circle patterns on surfaces and proved their rigidity. In this paper, we prove the existence of Guo-Luo's generalized circle patterns with prescribed generalized intersection angles on surfaces with cusps, which partially answers a question raised by Guo-Luo and generalizes Bobenko-Springborn's hyperbolic circle patterns on closed surfaces to generalized hyperbolic circle patterns on surfaces with cusps. We further introduce the combinatorial Ricci flow and combinatorial Calabi flow for generalized circle patterns on surfaces with cusps, and prove the longtime existence and convergence of the solutions for these combinatorial curvature flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09172 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized circle patterns on surfaces with cusps Xiong, Zhiwen Xu, Xu Geometric Topology Guo and Luo introduced generalized circle patterns on surfaces and proved their rigidity. In this paper, we prove the existence of Guo-Luo's generalized circle patterns with prescribed generalized intersection angles on surfaces with cusps, which partially answers a question raised by Guo-Luo and generalizes Bobenko-Springborn's hyperbolic circle patterns on closed surfaces to generalized hyperbolic circle patterns on surfaces with cusps. We further introduce the combinatorial Ricci flow and combinatorial Calabi flow for generalized circle patterns on surfaces with cusps, and prove the longtime existence and convergence of the solutions for these combinatorial curvature flows. |
| title | Generalized circle patterns on surfaces with cusps |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2504.09172 |