{"title":"Polar tangential angles and free elasticae","authors":"Tatsuya Miura","doi":"10.3934/MINE.2021034","DOIUrl":null,"url":null,"abstract":"In this note we investigate the behavior of the polar tangential angle of a general plane curve, and in particular prove its monotonicity for certain curves of monotone curvature. As an application we give (non)existence results for an obstacle problem involving free elasticae.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"89 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/MINE.2021034","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
In this note we investigate the behavior of the polar tangential angle of a general plane curve, and in particular prove its monotonicity for certain curves of monotone curvature. As an application we give (non)existence results for an obstacle problem involving free elasticae.
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