离散共形几何的收敛与均匀化映射的计算

IF 0.5 4区数学 Q3 MATHEMATICS

Asian Journal of Mathematics Pub Date : 2019-01-01 DOI:10.4310/AJM.2019.V23.N1.A2

D. Gu, F. Luo, Tianqi Wu

{"title":"离散共形几何的收敛与均匀化映射的计算","authors":"D. Gu, F. Luo, Tianqi Wu","doi":"10.4310/AJM.2019.V23.N1.A2","DOIUrl":null,"url":null,"abstract":"The classical uniformization theorem of Poincaré and Koebe states that any simply connected surface with a Riemannian metric is conformally diffeomorphic to the Riemann sphere, or the complex plane or the unit disk. Using the work by Gu-Luo-Sun-Wu [9] on discrete conformal geometry for polyhedral surfaces, we show that the uniformization maps for simply connected Riemann surfaces are computable.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"37","resultStr":"{\"title\":\"Convergence of discrete conformal geometry and computation of uniformization maps\",\"authors\":\"D. Gu, F. Luo, Tianqi Wu\",\"doi\":\"10.4310/AJM.2019.V23.N1.A2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The classical uniformization theorem of Poincaré and Koebe states that any simply connected surface with a Riemannian metric is conformally diffeomorphic to the Riemann sphere, or the complex plane or the unit disk. Using the work by Gu-Luo-Sun-Wu [9] on discrete conformal geometry for polyhedral surfaces, we show that the uniformization maps for simply connected Riemann surfaces are computable.\",\"PeriodicalId\":55452,\"journal\":{\"name\":\"Asian Journal of Mathematics\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"37\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asian Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/AJM.2019.V23.N1.A2\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/AJM.2019.V23.N1.A2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 37

摘要

庞加莱和柯比的经典均匀化定理指出，任何具有黎曼度规的单连通曲面都与黎曼球、复平面或单位盘共形微分同态。利用guu - luo - sun - wu[9]在多面体曲面的离散共形几何上的工作，我们证明了单连通黎曼曲面的均匀化映射是可计算的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Convergence of discrete conformal geometry and computation of uniformization maps

The classical uniformization theorem of Poincaré and Koebe states that any simply connected surface with a Riemannian metric is conformally diffeomorphic to the Riemann sphere, or the complex plane or the unit disk. Using the work by Gu-Luo-Sun-Wu [9] on discrete conformal geometry for polyhedral surfaces, we show that the uniformization maps for simply connected Riemann surfaces are computable.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊