{"title":"A note on minimal surfaces with bounded index","authors":"Maximo,Davi","doi":"10.4310/cag.2023.v31.n5.a1","DOIUrl":null,"url":null,"abstract":"For any closed Riemannian three-manifold, we prove that for any sequence of closed embedded minimal surfaces with uniformly bounded index, the genus can only grow at most linearly with respect to the area.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cag.2023.v31.n5.a1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
For any closed Riemannian three-manifold, we prove that for any sequence of closed embedded minimal surfaces with uniformly bounded index, the genus can only grow at most linearly with respect to the area.
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