Numerical computation of surface conformal mappings

Xianfeng David Gu; Wei Zeng; Feng Luo; Shing Tung Yau

doi:10.1007/bf03321885

Numerical computation of surface conformal mappings

Xianfeng David Gu, Wei Zeng, Feng Luo, Shing Tung Yau

School of Arts and Sciences, Mathematics

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

37 Scopus citations

Abstract

We report recent progress in the computation of conformal mappings from surfaces with arbitrary topologies to canonical domains. Two major computational methodologies are emphasized; one is holomorphic differentials based on Riemann surface theory and the other is surface Ricci ow from geometric analysis. The applications of surface conformal mapping in the field of engineering are briey reviewed.

Original language	English (US)
Pages (from-to)	747-787
Number of pages	41
Journal	Computational Methods and Function Theory
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/bf03321885
State	Published - Jan 2012

All Science Journal Classification (ASJC) codes

Analysis
Computational Theory and Mathematics
Applied Mathematics

Keywords

Conformal geometry
Discrete surface
Holomorphic differential
Ricci flow

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10.1007/bf03321885

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title = "Numerical computation of surface conformal mappings",

abstract = "We report recent progress in the computation of conformal mappings from surfaces with arbitrary topologies to canonical domains. Two major computational methodologies are emphasized; one is holomorphic differentials based on Riemann surface theory and the other is surface Ricci ow from geometric analysis. The applications of surface conformal mapping in the field of engineering are briey reviewed.",

keywords = "Conformal geometry, Discrete surface, Holomorphic differential, Ricci flow",

author = "Gu, {Xianfeng David} and Wei Zeng and Feng Luo and Yau, {Shing Tung}",

note = "Funding Information: Received June 21, 2011, in revised form August 16, 2011. Published online October 12, 2011. The research has been supported by NSF CCF-0448399, NSF DMS-0528363, NSF DMS-0626223, NSF IIS-0713145, NSF CCF-0830550, NSF CCF-0841514, ONR N000140910228, NSF III 0916286, NSF CCF-1081424, NSF Nets 1016829, NIH R01EB7530, and NSFC 60628202.",

year = "2012",

month = jan,

doi = "10.1007/bf03321885",

language = "English (US)",

volume = "11",

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AU - Gu, Xianfeng David

AU - Zeng, Wei

AU - Luo, Feng

AU - Yau, Shing Tung

N1 - Funding Information: Received June 21, 2011, in revised form August 16, 2011. Published online October 12, 2011. The research has been supported by NSF CCF-0448399, NSF DMS-0528363, NSF DMS-0626223, NSF IIS-0713145, NSF CCF-0830550, NSF CCF-0841514, ONR N000140910228, NSF III 0916286, NSF CCF-1081424, NSF Nets 1016829, NIH R01EB7530, and NSFC 60628202.

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N2 - We report recent progress in the computation of conformal mappings from surfaces with arbitrary topologies to canonical domains. Two major computational methodologies are emphasized; one is holomorphic differentials based on Riemann surface theory and the other is surface Ricci ow from geometric analysis. The applications of surface conformal mapping in the field of engineering are briey reviewed.

AB - We report recent progress in the computation of conformal mappings from surfaces with arbitrary topologies to canonical domains. Two major computational methodologies are emphasized; one is holomorphic differentials based on Riemann surface theory and the other is surface Ricci ow from geometric analysis. The applications of surface conformal mapping in the field of engineering are briey reviewed.

KW - Conformal geometry

KW - Discrete surface

KW - Holomorphic differential

KW - Ricci flow

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Numerical computation of surface conformal mappings

Abstract

All Science Journal Classification (ASJC) codes

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