论文标题
理想的三角剖分和磁盘的展开
Ideal Triangulation and Disk Unfolding of a Singular Flat Surface
论文作者
论文摘要
单一平坦表面的理想三角剖分是一个测量三角剖分，其顶点集等于表面的单数点。利用一个事实是，表面中的每对点具有有限数量的地球化物，其长度为$ \ leq l $将它们连接起来，其中$ l $是任何正数，我们证明每个奇异的平面表面都有理想的三角剖分，只要表面没有边界组件，或者每个边界组件的每个边界组件都具有单数点，或者其边界组件的每个边界都具有奇异的点。另外，我们证明了这样的表面包含有限数量的大地测量学，它们连接其奇异点，因此当我们通过这些弧线切割表面时，我们获得了一个具有非单明性内部的扁平磁盘。
An ideal triangulation of a singular flat surface is a geodesic triangulation such that its vertex set is equal to the set of singular points of the surface. Using the fact that each pair of points in a surface has a finite number of geodesics having length $\leq L$ connecting them, where $L$ is any positive number, we prove that each singular flat surface has an ideal triangulation provided that the surface has singular points when it has no boundary components, or each of its boundary components has a singular point. Also, we prove that such a surface contains a finite number of geodesics which connect its singular points so that when we cut the surface through these arcs we get a flat disk with a non-singular interior.
