{"title":"Interpolation inequalities between the deviation of curvature and the isoperimetric ratio with applications to geometric flows","authors":"Takeyuki Nagasawa, Kohei Nakamura","doi":"10.57262/ade/1565661673","DOIUrl":null,"url":null,"abstract":"Several inequalities for the isoperimetric ratio for plane curves are derived. In particular, we obtain interpolation inequalities between the deviation of curvature and the isoperimetric ratio. As applications, we study the large-time behavior of some geometric flows of closed plane curves without a convexity assumption.","PeriodicalId":53312,"journal":{"name":"Advances in Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2018-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.57262/ade/1565661673","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 5
Abstract
Several inequalities for the isoperimetric ratio for plane curves are derived. In particular, we obtain interpolation inequalities between the deviation of curvature and the isoperimetric ratio. As applications, we study the large-time behavior of some geometric flows of closed plane curves without a convexity assumption.
期刊介绍：
Advances in Differential Equations will publish carefully selected, longer research papers on mathematical aspects of differential equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new and non-trivial. Emphasis will be placed on papers that are judged to be specially timely, and of interest to a substantial number of mathematicians working in this area.
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