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Discrete conformal
geometry of polyhedral surfaces and its convergence
Feng Luo, Jian Sun and Tianqi Wu |
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Geometry & Topology 26 (2022) 937–987
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Abstract |
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We prove a result on the convergence of discrete conformal maps to the Riemann mappings for Jordan domains. It is a counterpart of Rodin and 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 and 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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Keywords
polyhedral metrics, discrete conformal map, Riemann
mapping, triangulation, Delaunay triangulation, convex
polyhedra, discrete harmonic functions
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Mathematical Subject Classification 2010
Primary: 52C26, 53C44, 58E30
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References |
Publication
Received: 8 April 2018
Revised: 28 December 2020
Accepted: 8 February 2021
Published: 3 August 2022
Proposed: David Gabai
Seconded: Tobias H Colding, Dmitri Burago
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Authors |
| Feng Luo | |
| Department of Mathematics Rutgers University Piscataway, NJ United States |
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| Jian Sun | |
| Mathematical Science Center Tsinghua University Beijing China |
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| Tianqi Wu | |
| Center of Mathematical Sciences and
Applications Harvard University Cambridge, MA United States |
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