Discrete Conformal Geometry of Polyhedral Surfaces and Its Convergence
arXiv:2009.12706 · doi:10.2140/gt.2022.26.937
Abstract
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.
37 pages, 11 figures