{"title":"Stability of the ball under volume preserving fractional mean curvature flow","authors":"A. Cesaroni, M. Novaga","doi":"10.1515/acv-2022-0027","DOIUrl":null,"url":null,"abstract":"Abstract We consider the volume constrained fractional mean curvature flow of a nearly spherical set and prove long time existence and asymptotic convergence to a ball. The result applies in particular to convex initial data under the assumption of global existence. Similarly, we show exponential convergence to a constant for the fractional mean curvature flow of a periodic graph.","PeriodicalId":49276,"journal":{"name":"Advances in Calculus of Variations","volume":" ","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2022-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Calculus of Variations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/acv-2022-0027","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: 3
Abstract
Abstract We consider the volume constrained fractional mean curvature flow of a nearly spherical set and prove long time existence and asymptotic convergence to a ball. The result applies in particular to convex initial data under the assumption of global existence. Similarly, we show exponential convergence to a constant for the fractional mean curvature flow of a periodic graph.
期刊介绍：
Advances in Calculus of Variations publishes high quality original research focusing on that part of calculus of variation and related applications which combines tools and methods from partial differential equations with geometrical techniques.
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