{"title":"Some estimates on stable minimal hypersurfaces in Euclidean space","authors":"Luen-Fai Tam","doi":"arxiv-2409.04947","DOIUrl":null,"url":null,"abstract":"We derive some estimates for stable minimal hypersurfaces in $\\R^{n+1}$. The\nestimates are related to recent proofs of Bernstein theorems for complete\nstable minimal hypersurfaces in $\\R^{n+1}$ for $3\\le n\\le 5$ by Chodosh-Li,\nChodosh-Li-Minter-Stryker and Mazet. In particular, the estimates indicate that\nthe methods in their proofs may not work for $n=6$, which is observed also by\nAntonelli-Xu. The method of derivation in this work might also be applied to\nother problems.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"28 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.04947","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We derive some estimates for stable minimal hypersurfaces in $\R^{n+1}$. The
estimates are related to recent proofs of Bernstein theorems for complete
stable minimal hypersurfaces in $\R^{n+1}$ for $3\le n\le 5$ by Chodosh-Li,
Chodosh-Li-Minter-Stryker and Mazet. In particular, the estimates indicate that
the methods in their proofs may not work for $n=6$, which is observed also by
Antonelli-Xu. The method of derivation in this work might also be applied to
other problems.
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