Courant-sharp eigenvalues of the three-dimensional square torus

DOI10.1090/proc/13148zbMath1348.35147arXiv1511.04199OpenAlexW2962998916WikidataQ126174469 ScholiaQ126174469MaRDI QIDQ2814414

Corentin Léna

Publication date: 22 June 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.04199

zbMATH Keywords

torusisoperimetric problemnodal domainsCourant theoremPleijel theorem

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20)

Related Items

Courant-sharp eigenvalues of Neumann 2-rep-tiles ⋮ Courant-sharp eigenvalues of compact flat surfaces: Klein bottles and cylinders

Cites Work

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• Dirichlet Eigenfunctions of the Square Membrane: Courant’s Property, and A. Stern’s and Å. Pleijel’s Analyses
• Pleijel’s nodal domain theorem for free membranes
• The periodic isoperimetric problem
• On Spectral Minimal Partitions: the Case of the Sphere
• Dirichlet eigenfunctions on the cube, sharpening the Courant nodal inequality

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