{"title":"The anisotropic Bernstein problem","authors":"Connor Mooney, Yang Yang","doi":"10.1007/s00222-023-01222-4","DOIUrl":null,"url":null,"abstract":"Abstract We construct nonlinear entire anisotropic minimal graphs over $\\mathbb{R}^{4}$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math> , completing the solution to the anisotropic Bernstein problem. The examples we construct have a variety of growth rates, and our approach both generalizes to higher dimensions and recovers and elucidates known examples of nonlinear entire minimal graphs over $\\mathbb{R}^{n},\\, n \\geq 8$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>R</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>,</mml:mo> <mml:mspace /> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>8</mml:mn> </mml:math> .","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00222-023-01222-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract We construct nonlinear entire anisotropic minimal graphs over $\mathbb{R}^{4}$ R4 , completing the solution to the anisotropic Bernstein problem. The examples we construct have a variety of growth rates, and our approach both generalizes to higher dimensions and recovers and elucidates known examples of nonlinear entire minimal graphs over $\mathbb{R}^{n},\, n \geq 8$ Rn,n≥8 .
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