{"title":"Lower bounds for the area of the image of a circle","authors":"B. Klishchuk, R. Salimov","doi":"10.13108/2017-9-2-55","DOIUrl":null,"url":null,"abstract":"In the work we consider Q-homeomorphisms w.r.t p-modulus on the complex plane as p > 2. We obtain a lower bound for the area of the image of a circle under such mappings. We solve the extremal problem on minimizing the functional of the area of the image of a circle.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"27 1","pages":"55-61"},"PeriodicalIF":0.5000,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ufa Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13108/2017-9-2-55","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 12
Abstract
In the work we consider Q-homeomorphisms w.r.t p-modulus on the complex plane as p > 2. We obtain a lower bound for the area of the image of a circle under such mappings. We solve the extremal problem on minimizing the functional of the area of the image of a circle.
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