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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.12355 |
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| _version_ | 1866916846581579776 |
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| author | Ji, Bohao |
| author_facet | Ji, Bohao |
| contents | In this paper, we study the combinatorial Yamabe flow on infinite triangulated surfaces in Euclidean background geometry, aiming for solving discrete Yamabe problem on noncompact surfaces. Under suitable conditions, we establish the short-time existence and uniqueness of the flow. We further introduce an extended version of the flow and prove its long-time existence. As an application, we prove the convergence result of the Yamabe flow in the case of hexagonal triangulations of the plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12355 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The existence and uniqueness of infinite combinatorial Yamabe flows Ji, Bohao Differential Geometry In this paper, we study the combinatorial Yamabe flow on infinite triangulated surfaces in Euclidean background geometry, aiming for solving discrete Yamabe problem on noncompact surfaces. Under suitable conditions, we establish the short-time existence and uniqueness of the flow. We further introduce an extended version of the flow and prove its long-time existence. As an application, we prove the convergence result of the Yamabe flow in the case of hexagonal triangulations of the plane. |
| title | The existence and uniqueness of infinite combinatorial Yamabe flows |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2507.12355 |