Rigidity of the Delaunay triangulations of the plane
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913472556564480 |
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| author | Dai, Song Wu, Tianqi |
| author_facet | Dai, Song Wu, Tianqi |
| contents | We proved a rigidity result for Delaunay triangulations of the plane under Luo's discrete conformal change, extending previous results on hexagonal triangulations. Our result is a discrete analogue of the conformal rigidity of the plane. We followed Zhengxu He's analytical approach in his work on the rigidity of disk patterns, and developed a discrete Schwarz lemma and a discrete Liouville theorem. The main tools include conformal modulus, discrete extremal length, and maximum principles in discrete conformal geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02609 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rigidity of the Delaunay triangulations of the plane Dai, Song Wu, Tianqi Geometric Topology We proved a rigidity result for Delaunay triangulations of the plane under Luo's discrete conformal change, extending previous results on hexagonal triangulations. Our result is a discrete analogue of the conformal rigidity of the plane. We followed Zhengxu He's analytical approach in his work on the rigidity of disk patterns, and developed a discrete Schwarz lemma and a discrete Liouville theorem. The main tools include conformal modulus, discrete extremal length, and maximum principles in discrete conformal geometry. |
| title | Rigidity of the Delaunay triangulations of the plane |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2305.02609 |