Construction of conformal mappings by generalized polarization tensors

Kang Hyeonbae; Lee Hyundae; Lim Mikyoung

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Construction of conformal mappings by generalized polarization tensors

机译：通过广义极化张量构造共形映射

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摘要

We present a new systematic method to compute the Riemann mapping from the outside of the unit disc to the outside of a simply connected domain. We derive explicit relations between the coefficients of the Riemann mapping and the generalized polarization tensors associated with the domain. Because the generalized polarization tensors can be computed numerically, we are able to compute the coefficients of the Riemann mapping using these relations. Effectiveness of the method is validated by numerical examples. Copyright (c) 2014 John Wiley & Sons, Ltd.

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《Mathematical Methods in the Applied Sciences》 |2015年第9期|共8页
作者
Kang Hyeonbae; Lee Hyundae; Lim Mikyoung;
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正文语种 eng
中图分类数学;
关键词
Riemann mapping; generalized polarization tensor; numerical computation; Neumann-Poincare operator;

机译：黎曼映射;广义极化张量;数值计算;Neumann-Poincare算子;

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专利

1. Construction of conformal mappings by generalized polarization tensors [J] . Kang Hyeonbae, Lee Hyundae, Lim Mikyoung Mathematical Methods in the Applied Sciences . 2015,第9期

机译：通过广义极化张量构造共形映射
2. Generalized Weyl conformal curvature tensor of generalized Riemannian space [J] . Nenad O. Vesic Miskolc Mathematical Notes . 2019,第1期

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3. KELDYSH-LAVRENTIEV COUNTEREXAMPLE AND MEANS OF POWERS OF A CONFORMAL MAPPING. 1. CONSTRUCTION OF A MAPPING [J] . H. Hedenmalm, N. A. Shirokov Journal of Mathematical Sciences . 2012,第5期

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4. INFINITESIMAL CONFORMAL TRANSFORMATIONS OF RIEMANNIAN MANIFOLDS WHICH PRESERVE THE GENERALIZED EINSTEIN TENSOR [C] . CHEREVKO Yevhen, BEREZOVSKII Vladimir, NENKA Ruslana, Conference on Applied Mathematics . 2020

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7. Construction of conformal mappings by generalized polarization tensors [O] . Kang, Hyeonbae, Lee, Hyundae, Lim, Mikyoung 2013

机译：用广义极化张量构造共形映射

Construction of conformal mappings by generalized polarization tensors

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