{"title":"Classification of convex ancient free-boundary curve-shortening flows in the disc","authors":"Theodora Bourni, Mat Langford","doi":"10.2140/apde.2023.16.2225","DOIUrl":null,"url":null,"abstract":"<p>Using a combination of direct geometric methods and an analysis of the linearization of the flow about the horizontal bisector, we prove that there exists a unique (modulo rotations about the origin) convex ancient curve-shortening flow in the disc with free boundary on the circle. This appears to be the first result of its kind in the free-boundary setting. </p>","PeriodicalId":49277,"journal":{"name":"Analysis & PDE","volume":"71 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis & PDE","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/apde.2023.16.2225","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Using a combination of direct geometric methods and an analysis of the linearization of the flow about the horizontal bisector, we prove that there exists a unique (modulo rotations about the origin) convex ancient curve-shortening flow in the disc with free boundary on the circle. This appears to be the first result of its kind in the free-boundary setting.
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APDE aims to be the leading specialized scholarly publication in mathematical analysis. The full editorial board votes on all articles, accounting for the journal’s exceptionally high standard and ensuring its broad profile.
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