{"title":"One property of a planar curve whose convex hull covers a given convex figure","authors":"Y. Nikonorov, Y. Nikonorova","doi":"10.4171/EM/458","DOIUrl":null,"url":null,"abstract":"In this note, we prove the following conjecture by A. Akopyan and V. Vysotsky: If the convex hull of a planar curve $\\gamma$ covers a planar convex figure $K$, then $\\operatorname{length}(\\gamma) \\geq \\operatorname{per} (K) - \\operatorname{diam} (K)$. In addition, all cases of equality in this inequality are studied.","PeriodicalId":41994,"journal":{"name":"Elemente der Mathematik","volume":" ","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Elemente der Mathematik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/EM/458","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
In this note, we prove the following conjecture by A. Akopyan and V. Vysotsky: If the convex hull of a planar curve $\gamma$ covers a planar convex figure $K$, then $\operatorname{length}(\gamma) \geq \operatorname{per} (K) - \operatorname{diam} (K)$. In addition, all cases of equality in this inequality are studied.