Combinatorial p-th Calabi flow for finite and infinite ideal circle patterns
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910997935030272 |
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| author | Yang, Xiaorui Yu, Hao |
| author_facet | Yang, Xiaorui Yu, Hao |
| contents | This paper presents a comprehensive study of the combinatorial $p$-th Calabi flow for both finite and infinite ideal circle patterns. In the finite case, we establish a sharp criterion: the combinatorial $p$-th Calabi flow with $p>1$ converges if and only if a constant curvature metric exists in the underlying geometric background. In the infinite setting, we prove the long-time existence of solutions to the combinatorial $p$-th Calabi flow for $p \geq 2$, representing a significant advance in the theory of curvature flows on infinite structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07130 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Combinatorial p-th Calabi flow for finite and infinite ideal circle patterns Yang, Xiaorui Yu, Hao Geometric Topology Differential Geometry This paper presents a comprehensive study of the combinatorial $p$-th Calabi flow for both finite and infinite ideal circle patterns. In the finite case, we establish a sharp criterion: the combinatorial $p$-th Calabi flow with $p>1$ converges if and only if a constant curvature metric exists in the underlying geometric background. In the infinite setting, we prove the long-time existence of solutions to the combinatorial $p$-th Calabi flow for $p \geq 2$, representing a significant advance in the theory of curvature flows on infinite structures. |
| title | Combinatorial p-th Calabi flow for finite and infinite ideal circle patterns |
| topic | Geometric Topology Differential Geometry |
| url | https://arxiv.org/abs/2506.07130 |