The Schwarz-Christoffel mapping to bounded multiply connected polygonal domains
The Schwarz-Christoffel mapping to bounded multiply connected polygonal domains
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DOI：
10.1098/rspa.2005.1480
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发表时间：
2005-09-08
影响因子：
3.5
通讯作者：
Crowdy, D
中科院分区：
文献类型：
--
作者：
Crowdy, D
给出了从有界多连通圆域到有界多连通多边形域的广义Schwarz-Christoffel映射公式。采用了经典肖特基群理论。映射函数的导数公式包含与与圆形预像区域相关的肖特基群有关的肖特基-克莱因素数函数的幂的乘积。该公式自然地推广了已知的单连通和双连通多边形域的映射公式。
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.