{"title":"Min-max construction of prescribed mean curvature hypersurfaces in noncompact manifolds","authors":"Douglas Stryker","doi":"arxiv-2409.07330","DOIUrl":null,"url":null,"abstract":"We develop a min-max theory for hypersurfaces of prescribed mean curvature in\nnoncompact manifolds, applicable to prescription functions that do not change\nsign outside a compact set. We use this theory to prove new existence results\nfor closed prescribed mean curvature hypersurfaces in Euclidean space and\ncomplete finite area constant mean curvature hypersurfaces in finite volume\nmanifolds.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"118 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","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-2409.07330","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 develop a min-max theory for hypersurfaces of prescribed mean curvature in
noncompact manifolds, applicable to prescription functions that do not change
sign outside a compact set. We use this theory to prove new existence results
for closed prescribed mean curvature hypersurfaces in Euclidean space and
complete finite area constant mean curvature hypersurfaces in finite volume
manifolds.
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