非紧凑流形中规定平均曲率超曲面的最小-最大构造

arXiv - MATH - Differential Geometry Pub Date : 2024-09-11 DOI:arxiv-2409.07330

Douglas Stryker

{"title":"非紧凑流形中规定平均曲率超曲面的最小-最大构造","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":"{\"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}","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

摘要

我们为非紧凑流形中的规定平均曲率超曲面提出了一种最小-最大理论，适用于在紧凑集外不改变符号的规定函数。我们利用这一理论证明了欧几里得空间中封闭的规定平均曲率超曲面和有限体积流形中完整的有限面积恒定平均曲率超曲面的新存在性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Min-max construction of prescribed mean curvature hypersurfaces in noncompact manifolds

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Differential Geometry

自引率

0.00%

发文量