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Rigidity of the Hexagonal Delaunay Triangulated Plane

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Abstract

We show the rigidity of the hexagonal Delaunay triangulated plane under Luo’s PL conformality. As a consequence, we obtain a rigidity theorem for a particular type of locally finite convex ideal hyperbolic polyhedra.

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Acknowledgements

During the preparation of this article, we showed our results to Professor Feng Luo. He told us that he and his coauthors had already got similar rigidity results (but without posting them online), which had been submitted to a journal. We thank Professor Feng Luo and Tianqi Wu for helpful conversations and suggestions. We would also like to thank Xiaoxiao Zhang for drawing the pictures in the paper. The first author is supported by NSF of China (No. 11871283, No. 11971244, and No. 12071338). The second author is supported by NSF of China (No. 11871094). The second author would like to thank the hospitality of Chern Institute of Mathematics during his visit in Spring 2018 when he initiated this collaboration. The third author is supported by NSF of China (No. 11571185 and No. 11871283), China Scholarship Council (No. 201706135016), and the Fundamental Research Funds for the Central Universities, Nankai University (No. 63191506).

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Authors and Affiliations

  1. Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China

    Song Dai

  2. School of Mathematics, Renmin University of China, Beijing, 100872, China

    Huabin Ge

  3. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

    Shiguang Ma

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  1. Song Dai
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  2. Huabin Ge
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Correspondence to Shiguang Ma.

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Dai, S., Ge, H. & Ma, S. Rigidity of the Hexagonal Delaunay Triangulated Plane. Peking Math J 5, 1–20 (2022). https://doi.org/10.1007/s42543-021-00036-8

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  • DOI: https://doi.org/10.1007/s42543-021-00036-8

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