Convergences of Combinatorial Ricci Flows to Degenerated Circle Packings in Hyperbolic Background Geometry
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917719602888704 |
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| author | Hu, Guangming Lu, Sicheng Tan, Dong Zhong, Youliang Zhou, Puchun |
| author_facet | Hu, Guangming Lu, Sicheng Tan, Dong Zhong, Youliang Zhou, Puchun |
| contents | This paper investigates a kind of degenerated circle packings in hyperbolic background geometry. A main problem is whether a prescribed total geodesic curvature data can be realized by a degenerated circle packing or not. We fully characterize the sufficient and necessary conditions and show the uniqueness. Furthermore, we introduce the combinatoral Ricci flow to find the desired degenerated circle packed surface, analougus to the methods of Chow-Luo and Takatsu. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08496 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergences of Combinatorial Ricci Flows to Degenerated Circle Packings in Hyperbolic Background Geometry Hu, Guangming Lu, Sicheng Tan, Dong Zhong, Youliang Zhou, Puchun Differential Geometry Geometric Topology 52C26, 57M50 This paper investigates a kind of degenerated circle packings in hyperbolic background geometry. A main problem is whether a prescribed total geodesic curvature data can be realized by a degenerated circle packing or not. We fully characterize the sufficient and necessary conditions and show the uniqueness. Furthermore, we introduce the combinatoral Ricci flow to find the desired degenerated circle packed surface, analougus to the methods of Chow-Luo and Takatsu. |
| title | Convergences of Combinatorial Ricci Flows to Degenerated Circle Packings in Hyperbolic Background Geometry |
| topic | Differential Geometry Geometric Topology 52C26, 57M50 |
| url | https://arxiv.org/abs/2407.08496 |