On the classification of discrete conformal structures on surfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909290639392768 |
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| author | Xu, Xu Zheng, Chao |
| author_facet | Xu, Xu Zheng, Chao |
| contents | Glickenstein \cite{Glickenstein} and Glickenstein-Thomas \cite{GT} introduced the discrete conformal structures on surfaces in an axiomatic approach and studied its classification. In this paper, we give a full classification of the discrete conformal structures on surfaces, which completes Glickenstein-Thomas' classification. As a result, we find some new classes of discrete conformal structures on surfaces, including some of the generalized circle packing metrics introduced by Guo-Luo \cite{GL2}. The relationships between the discrete conformal structures on surfaces and the 3-dimensional hyperbolic geometry are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13223 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the classification of discrete conformal structures on surfaces Xu, Xu Zheng, Chao Differential Geometry Glickenstein \cite{Glickenstein} and Glickenstein-Thomas \cite{GT} introduced the discrete conformal structures on surfaces in an axiomatic approach and studied its classification. In this paper, we give a full classification of the discrete conformal structures on surfaces, which completes Glickenstein-Thomas' classification. As a result, we find some new classes of discrete conformal structures on surfaces, including some of the generalized circle packing metrics introduced by Guo-Luo \cite{GL2}. The relationships between the discrete conformal structures on surfaces and the 3-dimensional hyperbolic geometry are also discussed. |
| title | On the classification of discrete conformal structures on surfaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2307.13223 |