{"title":"m-超凸域的几何。","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":null,"pages":null},"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":"{\"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\":null,\"pages\":null},\"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}","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}
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.
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