Rigidity of the Delaunay triangulations of the plane

Song Dai; Tianqi Wu

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arXiv · 2305.02609

Rigidity of the Delaunay triangulations of the plane

Song Dai·Tianqi Wu

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Abstract

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.

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Song Dai, Tianqi Wu. 2023-05-04. Rigidity of the Delaunay triangulations of the plane. https://arxiv.org/abs/2305.02609

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