{"title":"Mapping onto circular arc polygons","authors":"P. R. Brown","doi":"10.1080/02781070412331329403","DOIUrl":null,"url":null,"abstract":"A numerical method is developed for computing the accessory parameter of the Schwarzian derivative of the univalent mappings onto certain circular arc polygons with orthogonal boundary arcs. The geometrical properties of these polygons are investigated rigorously. An application of this method makes it possible to compute numerically the hyperbolic metric density function for some multiply-connected planar domains; in particular the covering map of the plane minus a lattice of discs.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"15 2","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complex Variables, Theory and Application: An International Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/02781070412331329403","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 11
Abstract
A numerical method is developed for computing the accessory parameter of the Schwarzian derivative of the univalent mappings onto certain circular arc polygons with orthogonal boundary arcs. The geometrical properties of these polygons are investigated rigorously. An application of this method makes it possible to compute numerically the hyperbolic metric density function for some multiply-connected planar domains; in particular the covering map of the plane minus a lattice of discs.
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