Convergence of discrete conformal geometry and computation of uniformization maps

David Gu; Feng Luo; Tianqi Wu

doi:10.4310/AJM.2019.v23.n1.a2

Convergence of discrete conformal geometry and computation of uniformization maps

David Gu, Feng Luo, Tianqi Wu

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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 language	English (US)
Pages (from-to)	21-34
Number of pages	14
Journal	Asian Journal of Mathematics
Volume	23
Issue number	1
DOIs	https://doi.org/10.4310/AJM.2019.v23.n1.a2
State	Published - 2019

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

Keywords

Discrete conformal geometry
Polyhedral surfaces
Uniformizations and convergences

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10.4310/AJM.2019.v23.n1.a2

Cite this

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abstract = "The classical uniformization theorem of Poincar{\'e} 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.",

keywords = "Discrete conformal geometry, Polyhedral surfaces, Uniformizations and convergences",

author = "David Gu and Feng Luo and Tianqi Wu",

note = "Funding Information: Acknowledgement. Part of the work is supported by the National Science Foundation of USA (NSF-DMS 1405106 and NSF DMS-1418255). Funding Information: Part of the work is supported by the National Science Foundation of USA (NSF-DMS 1405106 and NSF DMS-1418255). Publisher Copyright: {\textcopyright} 2019 International Press.",

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N1 - Funding Information: Acknowledgement. Part of the work is supported by the National Science Foundation of USA (NSF-DMS 1405106 and NSF DMS-1418255). Funding Information: Part of the work is supported by the National Science Foundation of USA (NSF-DMS 1405106 and NSF DMS-1418255). Publisher Copyright: © 2019 International Press.

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N2 - 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.

AB - 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.

KW - Discrete conformal geometry

KW - Polyhedral surfaces

KW - Uniformizations and convergences

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Convergence of discrete conformal geometry and computation of uniformization maps

Abstract

All Science Journal Classification (ASJC) codes

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