Branched $α$-combinatorial Ricci flows on closed surfaces with Euler characteristic $χ\le 0$
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912464435675136 |
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| author | Li, Wenjun Liu, Rongyuan Chen, Guohao Lin, Aijin |
| author_facet | Li, Wenjun Liu, Rongyuan Chen, Guohao Lin, Aijin |
| contents | In this paper we introduce the branched $α$-flows on closed surfaces with Euler characteristic \(χ\leq 0\). Based on the strict convexity of the branched $α$-potentials, we establish the long time existence and convergence of the solutions to the branched $α$-flows, which generalizes Ge and Xu's main results \cite{2015,2015A} on the $α$-flows. In addtion, we study the prescribed curvature problems under the relaxed precondition $χ(M)\in \mathbb{Z}$ via alternative $α$-flows, establishing admissibility conditions for prescribed curvatures and their exponential convergence to target metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24762 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Branched $α$-combinatorial Ricci flows on closed surfaces with Euler characteristic $χ\le 0$ Li, Wenjun Liu, Rongyuan Chen, Guohao Lin, Aijin Differential Geometry In this paper we introduce the branched $α$-flows on closed surfaces with Euler characteristic \(χ\leq 0\). Based on the strict convexity of the branched $α$-potentials, we establish the long time existence and convergence of the solutions to the branched $α$-flows, which generalizes Ge and Xu's main results \cite{2015,2015A} on the $α$-flows. In addtion, we study the prescribed curvature problems under the relaxed precondition $χ(M)\in \mathbb{Z}$ via alternative $α$-flows, establishing admissibility conditions for prescribed curvatures and their exponential convergence to target metrics. |
| title | Branched $α$-combinatorial Ricci flows on closed surfaces with Euler characteristic $χ\le 0$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2505.24762 |