Numerical Conformal Mapping to One-Tooth Gear-Shaped Domains and Applications

We study conformal mappings from the unit disk (or a rectangle) to one-tooth gear-shaped planar domains from the point of view of the Schwarzian derivative, with emphasis on numerical considerations. Applications are given to evaluation of a singular integral, mapping to the complement of an annular...

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Veröffentlicht in:	Computational methods and function theory 2016-06, Vol.16 (2), p.319-345
Hauptverfasser:	Brown, Philip R., Porter, R. Michael
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Computational Mathematics and Numerical Analysis Functions of a Complex Variable Mathematics Mathematics and Statistics
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Beschreibung
Zusammenfassung:	We study conformal mappings from the unit disk (or a rectangle) to one-tooth gear-shaped planar domains from the point of view of the Schwarzian derivative, with emphasis on numerical considerations. Applications are given to evaluation of a singular integral, mapping to the complement of an annular rectangle, and symmetric multitooth domains.
ISSN:	1617-9447 2195-3724
DOI:	10.1007/s40315-015-0149-4