Convergence of discrete conformal geometry and computation of uniformization maps

David Gu, Feng Luo, Tianqi Wu

Research output: Contribution to journalArticle

Abstract

The classical uniformization theorem of Poincaré and Koebe states that any simply connected surface with a Riemannian metric is conformally diffeomorphic to the Riemann sphere, or the complex plane or the unit disk. Using the work by Gu-Luo-Sun-Wu [9] on discrete conformal geometry for polyhedral surfaces, we show that the uniformization maps for simply connected Riemann surfaces are computable.

Original languageEnglish (US)
Pages (from-to)21-34
Number of pages14
JournalAsian Journal of Mathematics
Volume23
Issue number1
DOIs
StatePublished - Jan 1 2019

Fingerprint

Conformal Geometry
Discrete Geometry
Uniformization
Geometry
Riemannian Metric
Sun
Riemann Surface
Argand diagram
Unit Disk
Theorem

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Discrete conformal geometry
  • Polyhedral surfaces
  • Uniformizations and convergences

Cite this

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Convergence of discrete conformal geometry and computation of uniformization maps. / Gu, David; Luo, Feng; Wu, Tianqi.

In: Asian Journal of Mathematics, Vol. 23, No. 1, 01.01.2019, p. 21-34.

Research output: Contribution to journalArticle

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AU - Luo, Feng

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KW - Uniformizations and convergences

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