平面锐角三角剖分的刚性
Rigidity of Acute Triangulations of the Plane
摘要：
我们证明了一个统一的锐角三角剖分的平面是刚性的罗的离散保形变化下，扩展以前的结果六边形三角剖分。我们的结果是一个离散模拟的共形刚度的平面。我们遵循他的分析方法在他的工作刚性磁盘模式。主要工具包括最大值原理，离散刘维尔定理，光滑和离散网络上的极值长度。关键是将欧氏离散共形性与双曲离散共形性联系起来，得到离散共形因子的L-无穷界。
英文摘要：
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.
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