{"title":"The Geometry of <i>m</i>-Hyperconvex Domains.","authors":"Per Åhag, Rafał Czyż, Lisa Hed","doi":"10.1007/s12220-017-9957-2","DOIUrl":null,"url":null,"abstract":"<p><p>We study the geometry of <i>m</i>-regular domains within the Caffarelli-Nirenberg-Spruck model in terms of barrier functions, envelopes, exhaustion functions, and Jensen measures. We prove among other things that every <i>m</i>-hyperconvex domain admits an exhaustion function that is negative, smooth, strictly <i>m</i>-subharmonic, and has bounded <i>m</i>-Hessian measure.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"28 4","pages":"3196-3222"},"PeriodicalIF":1.2000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-017-9957-2","citationCount":"22","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Geometric Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12220-017-9957-2","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2017/11/16 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 22
Abstract
We study the geometry of m-regular domains within the Caffarelli-Nirenberg-Spruck model in terms of barrier functions, envelopes, exhaustion functions, and Jensen measures. We prove among other things that every m-hyperconvex domain admits an exhaustion function that is negative, smooth, strictly m-subharmonic, and has bounded m-Hessian measure.
期刊介绍：
JGA publishes both research and high-level expository papers in geometric analysis and its applications. There are no restrictions on page length.
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