The Schwarz-Christoffel mapping to bounded multiply connected polygonal domains

被引：72

作者：

Crowdy, D ^{[1
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2005年 / 461卷 / 2061期

关键词：

conformal mapping; Schwarz-Christoffel; multiply connected;

D O I：

10.1098/rspa.2005.1480

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

A formula for the generalized Schwarz-Christoffel mapping from a bounded multiply connected circular domain to a bounded multiply connected polygonal domain is derived. The theory of classical Schottky groups is employed. The formula for the derivative of the mapping function contains a product of powers of Schottky-Klein prime functions associated with a Schottky group relevant to the circular pre-image domain. The formula generalizes, in a natural way, the known mapping formulae for simply and doubly connected polygonal domains.

引用

页码：2653 / 2678

页数：26

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PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2005, 461 (2060) :2477-2501

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