Discrete conformal geometry of polyhedral surfaces and its convergence

Feng Luo, Jian Sun, Tianqi Wu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)937-987
Number of pages51
JournalGeometry and Topology
Volume26
Issue number3
DOIs
StatePublished - Aug 3 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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