论文标题
与边界表面上广义圆形包装的组合曲率流
Combinatorial curvature flows for generalized circle packings on surfaces with boundary
论文作者
论文摘要
在本文中，我们研究了具有边界的理想三角形表面上的广义圆包装的变形，这是$（-1，-1，-1）$ type type gentrized Circle填料指标，由Guo-luo \ cite {gl2}引入。为了在规定长度的完全测量边界的表面上找到双曲线指标，我们引入了组合RICCI流动和组合Calabi流动，用于在理想地具有边界的三角形表面上的广义圆圈。然后，我们证明了这些组合曲率流的解决方案的长期存在和全局融合，这些曲率流提供了有效的算法，可在具有完全大地的长度的地球界面上查找双曲线指标。
In this paper, we investigate the deformation of generalized circle packings on ideally triangulated surfaces with boundary, which is the $(-1,-1,-1)$ type generalized circle packing metric introduced by Guo-Luo \cite{GL2}. To find hyperbolic metrics on surfaces with totally geodesic boundaries of prescribed lengths, we introduce combinatorial Ricci flow and combinatorial Calabi flow for generalized circle packings on ideally triangulated surfaces with boundary. Then we prove the longtime existence and global convergence for the solutions of these combinatorial curvature flows, which provide effective algorithms for finding hyperbolic metrics on surfaces with totally geodesic boundaries of prescribed lengths.
