{"title":"论黎曼流形中恒定高阶平均曲率超曲面的稳定性","authors":"Maria Fernanda Elbert, Barbara Nelli","doi":"10.1002/mana.202400159","DOIUrl":null,"url":null,"abstract":"<p>We propose a notion of stability for constant <span></span><math>\n <semantics>\n <mi>k</mi>\n <annotation>$k$</annotation>\n </semantics></math>-mean curvature hypersurfaces in a general Riemannian manifold and we give some applications. When the ambient manifold is a Space Form, our notion coincides with the known one, given by means of the variational problem.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 11","pages":"4031-4043"},"PeriodicalIF":0.8000,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the stability of constant higher order mean curvature hypersurfaces in a Riemannian manifold\",\"authors\":\"Maria Fernanda Elbert, Barbara Nelli\",\"doi\":\"10.1002/mana.202400159\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We propose a notion of stability for constant <span></span><math>\\n <semantics>\\n <mi>k</mi>\\n <annotation>$k$</annotation>\\n </semantics></math>-mean curvature hypersurfaces in a general Riemannian manifold and we give some applications. When the ambient manifold is a Space Form, our notion coincides with the known one, given by means of the variational problem.</p>\",\"PeriodicalId\":49853,\"journal\":{\"name\":\"Mathematische Nachrichten\",\"volume\":\"297 11\",\"pages\":\"4031-4043\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematische Nachrichten\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mana.202400159\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Nachrichten","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202400159","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the stability of constant higher order mean curvature hypersurfaces in a Riemannian manifold
We propose a notion of stability for constant -mean curvature hypersurfaces in a general Riemannian manifold and we give some applications. When the ambient manifold is a Space Form, our notion coincides with the known one, given by means of the variational problem.
期刊介绍：
Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index
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