Combinatorial Ricci flows on infinite disk triangulations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908306783600640 |
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| author | Ge, Huabin Hua, Bobo Zhou, Puchun |
| author_facet | Ge, Huabin Hua, Bobo Zhou, Puchun |
| contents | In this paper, we introduce combinatorial Ricci flows (CRFs in short) in Euclidean and hyperbolic background geometries on infinite triangulations of the open disk, which are discrete analogs of Ricci flows on simply connected open surfaces. We establish well-posedness results, the existence and the uniqueness, of CRFs in both Euclidean and hyperbolic background geometries. Moreover, we prove convergence results of CRFs, which indicate a uniformization theorem for CRFs on infinite disk triangulations. As an application, we prove an existence result of circle-packing metrics with infinite prescribed cone angles in hyperbolic background geometry. To our knowledge, these are the first results of CRFs on infinite triangulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05817 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Combinatorial Ricci flows on infinite disk triangulations Ge, Huabin Hua, Bobo Zhou, Puchun Geometric Topology Differential Geometry 52C26, 51M10, 57M50 In this paper, we introduce combinatorial Ricci flows (CRFs in short) in Euclidean and hyperbolic background geometries on infinite triangulations of the open disk, which are discrete analogs of Ricci flows on simply connected open surfaces. We establish well-posedness results, the existence and the uniqueness, of CRFs in both Euclidean and hyperbolic background geometries. Moreover, we prove convergence results of CRFs, which indicate a uniformization theorem for CRFs on infinite disk triangulations. As an application, we prove an existence result of circle-packing metrics with infinite prescribed cone angles in hyperbolic background geometry. To our knowledge, these are the first results of CRFs on infinite triangulations. |
| title | Combinatorial Ricci flows on infinite disk triangulations |
| topic | Geometric Topology Differential Geometry 52C26, 51M10, 57M50 |
| url | https://arxiv.org/abs/2504.05817 |