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

Computer Science

Stony Brook University

Stony Brook University
Rutgers - The State University of New Jersey, New Brunswick
Harvard University

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

49 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
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

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\}",

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volume = "11",

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AU - Gu, Xianfeng David

AU - Zeng, Wei

AU - Luo, Feng

AU - Yau, Shing Tung

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Y1 - 2012/1

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

UR - https://www.scopus.com/pages/publications/84857211317

U2 - 10.1007/bf03321885

DO - 10.1007/bf03321885

M3 - Article

SN - 1617-9447

VL - 11

SP - 747

EP - 787

JO - Computational Methods and Function Theory

JF - Computational Methods and Function Theory

IS - 2

ER -

Numerical computation of surface conformal mappings

Abstract

Keywords

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