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Rigidity of Acute Triangulations of the Plane | | Tianqi Wu
; | | Date: |
1 Aug 2022 | | Abstract: | We show that a uniformly acute triangulation of the plane is rigid 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 He’s analytical approach in his work on the rigidity of
disk patterns. The main tools include maximum principles, a discrete Liouville
theorem, smooth and discrete extremal lengths on networks. The key step is
relating the Euclidean discrete conformality to the hyperbolic discrete
conformality, to obtain an L-infinity bound on the discrete conformal factor. | | Source: | arXiv, 2208.00580 | | Services: | Forum | Review | PDF | Favorites | |
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