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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2208.04502 |
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| _version_ | 1866918061872775168 |
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| author | Luo, Yanwen Xu, Xu Zheng, Chao |
| author_facet | Luo, Yanwen Xu, Xu Zheng, Chao |
| contents | In this paper, maximum principles for Euclidean and hyperbolic discrete conformal structures on polyhedral surfaces are established. These maximum principles unify and generalize the maximum principles for vertex scalings and different types of circle packings in the literature. As an application of the hyperbolic discrete maximum principle, a discrete Schwarz-Ahlfors lemma is established. As another application, an infinite rigidity theorem for small Delaunay triangulations of the hyperbolic plane is proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_04502 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Maximal principles in discrete conformal geometry with application to the rigidity of infinite triangulations Luo, Yanwen Xu, Xu Zheng, Chao Metric Geometry In this paper, maximum principles for Euclidean and hyperbolic discrete conformal structures on polyhedral surfaces are established. These maximum principles unify and generalize the maximum principles for vertex scalings and different types of circle packings in the literature. As an application of the hyperbolic discrete maximum principle, a discrete Schwarz-Ahlfors lemma is established. As another application, an infinite rigidity theorem for small Delaunay triangulations of the hyperbolic plane is proved. |
| title | Maximal principles in discrete conformal geometry with application to the rigidity of infinite triangulations |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2208.04502 |