Discrete conformal geometry of polyhedral surfaces and its convergence
Discrete conformal geometry of polyhedral surfaces and its convergence
复制标题
DOI：
10.2140/gt.2022.26.937
复制
发表时间：
2020-09
期刊：
影响因子：
--
通讯作者：
F. Luo;Jian Sun;Tianqi Wu
中科院分区：
文献类型：
--
作者：
F. Luo;Jian Sun;Tianqi Wu
一辆BSTRACT。证明了Jordan区域上离散共形映射收敛到Riemann映射的一个结果。它是Rodin-Sullivan关于圆填充映射在离散保形的新背景下收敛到Riemann映射的一个对应定理。证明遵循了Rodin-Sullivan使用的相同策略，即建立了平面正则六角形三角剖分的刚性结果，并估计了与离散保角映射相关的拟共形常数。
A BSTRACT . The paper proves a result on the convergence of discrete conformal maps to the Riemann mappings for Jordan domains. It is a counterpart of Rodin-Sullivan’s theorem on convergence of circle packing mappings to the Riemann mapping in the new setting of discrete conformality. The proof follows the same strategy that Rodin-Sullivan used by establishing a rigidity result for regular hexagonal triangulations of the plane and estimating the quasiconformal constants associated to the discrete conformal maps.