Infinite combinatorial Ricci flow in spherical background geometry
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909610036690944 |
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| author | Li, Chang Lu, Yangxiang Yu, Hao |
| author_facet | Li, Chang Lu, Yangxiang Yu, Hao |
| contents | Since the fundamental work of Chow-Luo \cite{CL03}, Ge \cite{Ge12,Ge17} et al., the combinatorial curvature flow methods became a basic technique in the study of circle pattern theory. In this paper, we investigate the combinatorial Ricci flow with prescribed total geodesic curvatures in spherical background geometry. For infinite cellular decompositions, we establish the existence of a solution to the flow equation for all time. Furthermore, under an additional condition, we prove that the solution converges as time tends to infinity. To the best of our knowledge, this is the first study of an infinite combinatorial curvature flow in spherical background geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05925 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite combinatorial Ricci flow in spherical background geometry Li, Chang Lu, Yangxiang Yu, Hao Geometric Topology Differential Geometry 52C26, 51M10, 57M50 Since the fundamental work of Chow-Luo \cite{CL03}, Ge \cite{Ge12,Ge17} et al., the combinatorial curvature flow methods became a basic technique in the study of circle pattern theory. In this paper, we investigate the combinatorial Ricci flow with prescribed total geodesic curvatures in spherical background geometry. For infinite cellular decompositions, we establish the existence of a solution to the flow equation for all time. Furthermore, under an additional condition, we prove that the solution converges as time tends to infinity. To the best of our knowledge, this is the first study of an infinite combinatorial curvature flow in spherical background geometry. |
| title | Infinite combinatorial Ricci flow in spherical background geometry |
| topic | Geometric Topology Differential Geometry 52C26, 51M10, 57M50 |
| url | https://arxiv.org/abs/2505.05925 |