{"title":"球凸函数的Schwarz引理的几何版本","authors":"Maria Kourou, Oliver Roth","doi":"10.4153/S0008414X22000529","DOIUrl":null,"url":null,"abstract":"Abstract We prove several sharp distortion and monotonicity theorems for spherically convex functions defined on the unit disk involving geometric quantities such as spherical length, spherical area, and total spherical curvature. These results can be viewed as geometric variants of the classical Schwarz lemma for spherically convex functions.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Geometric versions of Schwarz’s lemma for spherically convex functions\",\"authors\":\"Maria Kourou, Oliver Roth\",\"doi\":\"10.4153/S0008414X22000529\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We prove several sharp distortion and monotonicity theorems for spherically convex functions defined on the unit disk involving geometric quantities such as spherical length, spherical area, and total spherical curvature. These results can be viewed as geometric variants of the classical Schwarz lemma for spherically convex functions.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-04-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4153/S0008414X22000529\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4153/S0008414X22000529","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Geometric versions of Schwarz’s lemma for spherically convex functions
Abstract We prove several sharp distortion and monotonicity theorems for spherically convex functions defined on the unit disk involving geometric quantities such as spherical length, spherical area, and total spherical curvature. These results can be viewed as geometric variants of the classical Schwarz lemma for spherically convex functions.
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