论文标题
平面急性三角形的刚度
Rigidity of Acute Triangulations of the Plane
论文作者
论文摘要
我们表明，在Luo离散的共形变化下，平面均匀的急性三角剖分是刚性的，从而扩展了对六边形三角剖分的先前结果。我们的结果是平面刚性的离散类似物。我们遵循了他在磁盘模式刚度的工作中的分析方法。主要工具包括最大原则，离散的liouville定理，网络上的平滑和离散的极端长度。关键步骤是将欧几里得离散的保密性与双曲线离散形式相关联，以获得离散的共形因子结合的l-赋值。
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.
