Rigidity of Infinite Hexagonal Triangulation of the Plane

Rigidity of the hexagonal Delaunay triangulated plane

We show the rigidity of the hexagonal Delaunay triangulated plane under Luo's PL conformality. As a consequence, we obtain a rigidity theorem for a particular type of locally finite convex ideal hyperbolic polyhedra.

无穷六边形三角剖分上Doyle圆填充的刚性

The rigidity of Doyle circle packings on the infinite hexagonal triangulation

本文针对Doyle猜想，通过发现相邻圆半径比的对数为加权离散调和函数，利用离散调和函数的Liouville定理，证明了半径比一致有界的六边形格点无穷圆填充中Doyle螺线的刚性，给出猜想的部分解答。

六边形几何三角剖分

Hexagonal Geometric Triangulations

本文构造了双曲平面的6-正则测地三角剖分，填补了该正则度在双曲平面上的空白。

平面Delaunay三角剖分的刚性

Rigidity of the Delaunay triangulations of the plane

本研究证明平面Delaunay三角剖分在Luo离散共形变换下的刚性，拓展六边形三角剖分相关结果，通过离散Schwarz引理等工具，建立平面共形刚性的离散对应版本。

Rigidity of Acute Triangulations of the Plane

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 …

非紧曲面、三角剖分与刚性

Noncompact surfaces, triangulations and rigidity

本文证明了每个非紧曲面均存在极小3-刚性的(3,6)-紧三角剖分，将其应用于R^3中可数杆-关节框架的通用刚性，并简化了Richards对Kerékjártó非紧曲面分类的证明。