Rigidity of Infinite Hexagonal Triangulation of the Plane

Tianqi Wu; Xianfeng Gu; Jian Sun

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arXiv · 1306.3630

Rigidity of Infinite Hexagonal Triangulation of the Plane

Tianqi Wu·Xianfeng Gu·Jian Sun

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Abstract

In the paper, we consider the rigidity problem of the infinite hexagonal triangulation of the plane under the piecewise linear conformal changes introduced by Luo in [5]. Our result shows that if a geometric hexagonal triangulation of the plane is PL conformal to the regular hexagonal triangulation and all inner angles are in $[δ, π/2 -δ]$ for any constant $δ> 0$, then it is the regular hexagonal triangulation. This partially solves a conjecture of Luo [4]. The proof uses the concept of \emph{quasi-harmonic} functions to unfold the properties of the mesh.

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BibTeX RIS

Tianqi Wu, Xianfeng Gu, Jian Sun. 2013-06-16. Rigidity of Infinite Hexagonal Triangulation of the Plane. https://arxiv.org/abs/1306.3630

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