{"title":"最小图增长的下限","authors":"Allen Weitsman","doi":"10.1007/s40315-024-00532-9","DOIUrl":null,"url":null,"abstract":"<p>We show that for minimal graphs in <span>\\(R^3\\)</span> having 0 boundary values over simpy connected domains, the maximum over circles of radius r must be at least of the order <span>\\(r^{1/2}\\)</span>.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Lower Bound on the Growth of Minimal Graphs\",\"authors\":\"Allen Weitsman\",\"doi\":\"10.1007/s40315-024-00532-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We show that for minimal graphs in <span>\\\\(R^3\\\\)</span> having 0 boundary values over simpy connected domains, the maximum over circles of radius r must be at least of the order <span>\\\\(r^{1/2}\\\\)</span>.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-04-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s40315-024-00532-9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40315-024-00532-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们证明，对于在简单连通域上边界值为 0 的 \(R^3\) 中的最小图，半径为 r 的圆上的最大值必须至少是 \(r^{1/2}\) 的数量级。
We show that for minimal graphs in \(R^3\) having 0 boundary values over simpy connected domains, the maximum over circles of radius r must be at least of the order \(r^{1/2}\).
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