{"title":"On the stochastically complete hypersurfaces in the product spaces Mn(κ)×R","authors":"Fábio R. dos Santos, Joicy P. Cruz","doi":"10.1016/j.jmaa.2025.129292","DOIUrl":null,"url":null,"abstract":"<div><div>A Simons-type equation for hypersurfaces in a product space <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>κ</mi><mo>)</mo><mo>×</mo><mi>R</mi></math></span>, where <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>κ</mi><mo>)</mo></math></span> is a Riemannian manifold with constant sectional curvature <em>κ</em>, is derived. Several applications are presented, including those for stochastically complete hypersurfaces with zero mean curvature and nonzero constant mean curvature in these spaces.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 2","pages":"Article 129292"},"PeriodicalIF":1.2000,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X25000733","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
A Simons-type equation for hypersurfaces in a product space , where is a Riemannian manifold with constant sectional curvature κ, is derived. Several applications are presented, including those for stochastically complete hypersurfaces with zero mean curvature and nonzero constant mean curvature in these spaces.
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