论文标题
CMC-1表面通过示意性Möbius转换
CMC-1 surfaces via osculating Möbius transformations between circle patterns
论文作者
论文摘要
给定平面中相同组合物的两个圆形模式，Möbius变换映射到一个到另一个的圆形映射culldisks a $ psl（2，\ mathbb {c}）$ - 在双图上的值。这样的功能起着示意性möbius转化的作用，并诱导双曲空间中双重图的实现。在两个圆图模式共享相同的剪切坐标或相同的相交角的情况下，我们表征了实现并获得一对一的对应关系。这些对应关系类似于具有恒定曲率$ h \ equiv 1 $在双曲空间中的表面的Weierstrass表示。我们进一步建立了三角形晶格的收敛性。
Given two circle patterns of the same combinatorics in the plane, the Möbius transformations mapping circumdisks of one to the other induces a $PSL(2,\mathbb{C})$-valued function on the dual graph. Such a function plays the role of an osculating Möbius transformation and induces a realization of the dual graph in hyperbolic space. We characterize the realizations and obtain a one-to-one correspondence in the cases that the two circle patterns share the same shear coordinates or the same intersection angles. These correspondences are analogous to the Weierstrass representation for surfaces with constant mean curvature $H\equiv 1$ in hyperbolic space. We further establish convergence on triangular lattices.
