Combinatorial Calabi flows with ideal circle patterns
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916549845057536 |
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| author | Zhang, Xiaoxiao |
| author_facet | Zhang, Xiaoxiao |
| contents | In this paper, we extend the work of Ge-Hua-Zhou \cite{GHZ} on combinatorial Ricci flows for ideal circle patterns to combinatorial Calabi flows in both hyperbolic and Euclidean background geometry. We prove the solution to the combinatorial Calabi flows with any given initial Euclidean (hyperbolic resp.)ideal circle pattern exists for all time and converges exponentially fast to a flat cone metric (hyperbolic resp.) on a given surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01605 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Combinatorial Calabi flows with ideal circle patterns Zhang, Xiaoxiao Differential Geometry Geometric Topology In this paper, we extend the work of Ge-Hua-Zhou \cite{GHZ} on combinatorial Ricci flows for ideal circle patterns to combinatorial Calabi flows in both hyperbolic and Euclidean background geometry. We prove the solution to the combinatorial Calabi flows with any given initial Euclidean (hyperbolic resp.)ideal circle pattern exists for all time and converges exponentially fast to a flat cone metric (hyperbolic resp.) on a given surface. |
| title | Combinatorial Calabi flows with ideal circle patterns |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2501.01605 |