A counterexample to Payne's nodal line conjecture with few holes

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dc.contributor.authorDahne, Joel
dc.contributor.authorGómez Serrano, Javier
dc.contributor.authorHou, Kimberly
dc.date.accessioned2026-06-17T16:38:10Z
dc.date.available2026-06-17T16:38:10Z
dc.date.issued2021
dc.date.updated2026-06-17T16:38:10Z
dc.description.abstractPayne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the boundary of the domain. In their 1997 breakthrough paper, Hoffmann-Ostenhof, Hoffmann-Ostenhof and Nadirashvili proved this to be false by constructing a counterexample in the plane with many holes and raised the question of the minimum number of holes a counterexample can have. In this paper we prove it is at most 6.
dc.format.extent13 p.
dc.format.mimetypeapplication/pdf
dc.identifier.idgrec722422
dc.identifier.issn1007-5704
dc.identifier.urihttps://hdl.handle.net/2445/230092
dc.language.isoeng
dc.publisherElsevier B.V.
dc.relation.isformatofReproducció del document publicat a: https://doi.org/10.1016/j.cnsns.2021.105957
dc.relation.ispartofCommunications In Nonlinear Science And Numerical Simulation, 2021, vol. 103, p. 105957
dc.relation.urihttps://doi.org/10.1016/j.cnsns.2021.105957
dc.rightscc-by-nc-nd (c) Dahne, Joel et al., 2021
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.sourceArticles publicats en revistes (Matemàtiques i Informàtica)
dc.subject.classificationTeorema de Noether
dc.subject.classificationCorbes modulars
dc.subject.otherNoether's theorem
dc.subject.otherModular curves
dc.titleA counterexample to Payne's nodal line conjecture with few holes
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion

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