{"title":"Estimates for the lowest Neumann eigenvalues of parallelograms and domains of constant width","authors":"Corentin Léna, Jonathan Rohleder","doi":"10.1007/s13324-024-00900-7","DOIUrl":null,"url":null,"abstract":"<div><p>We prove sharp upper bounds for the first and second non-trivial eigenvalues of the Neumann Laplacian in two classes of domains: parallelograms and domains of constant width. This gives in particular a new proof of an isoperimetric inequality for parallelograms recently obtained by A. Henrot, A. Lemenant and I. Lucardesi.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 3","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00900-7.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s13324-024-00900-7","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
We prove sharp upper bounds for the first and second non-trivial eigenvalues of the Neumann Laplacian in two classes of domains: parallelograms and domains of constant width. This gives in particular a new proof of an isoperimetric inequality for parallelograms recently obtained by A. Henrot, A. Lemenant and I. Lucardesi.
期刊介绍：
Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.
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