{"title":"Ancient solutions and translators of Lagrangian mean curvature flow","authors":"","doi":"10.1007/s10240-023-00143-5","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>Suppose that ℳ is an almost calibrated, exact, ancient solution of Lagrangian mean curvature flow in <span> <span>\\(\\mathbf {C} ^{n}\\)</span> </span>. We show that if ℳ has a blow-down given by the static union of two Lagrangian subspaces with distinct Lagrangian angles that intersect along a line, then ℳ is a translator. In particular in <span> <span>\\(\\mathbf {C} ^{2}\\)</span> </span>, all almost calibrated, exact, ancient solutions of Lagrangian mean curvature flow with entropy less than 3 are special Lagrangian, a union of planes, or translators.</p>","PeriodicalId":516319,"journal":{"name":"Publications mathématiques de l'IHÉS","volume":"9 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Publications mathématiques de l'IHÉS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s10240-023-00143-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
Suppose that ℳ is an almost calibrated, exact, ancient solution of Lagrangian mean curvature flow in \(\mathbf {C} ^{n}\). We show that if ℳ has a blow-down given by the static union of two Lagrangian subspaces with distinct Lagrangian angles that intersect along a line, then ℳ is a translator. In particular in \(\mathbf {C} ^{2}\), all almost calibrated, exact, ancient solutions of Lagrangian mean curvature flow with entropy less than 3 are special Lagrangian, a union of planes, or translators.
Abstract Suppose that ℳ is an almost calibrated, exact, ancient solution of Lagrangian mean curvature flow in \(\mathbf {C} ^{n}\) .我们证明，如果ℳ有一个由两个具有不同拉格朗日角的拉格朗日子空间的静态联合给出的吹落，并且这两个拉格朗日子空间沿着一条线相交，那么ℳ就是一个平移。特别是在\(\mathbf {C} ^{2}\)中，所有熵小于3的拉格朗日平均曲率流的几乎校准的、精确的、古老的解都是特殊的拉格朗日、平面的联合或平移器。
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