Discrete Conformal Geometry of Polyhedral Surfaces and Its Convergence

Feng Luo; Jian Sun; Tianqi Wu

doi:10.2140/gt.2022.26.937

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arXiv · 2009.12706

Discrete Conformal Geometry of Polyhedral Surfaces and Its Convergence

Feng Luo·Jian Sun·Tianqi Wu

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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.

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BibTeX RIS

Feng Luo, Jian Sun, Tianqi Wu. 2020-09-26. Discrete Conformal Geometry of Polyhedral Surfaces and Its Convergence. https://doi.org/10.2140/gt.2022.26.937

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