Isoperimetric inequalities for eigenvalues of triangles

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dc.creatorSiudeja, Bartłomiej
dc.date2007-07-24
dc.date2008-07-17
dc.date.accessioned2026-07-07T09:50:34Z
dc.date.available2026-07-07T09:50:34Z
dc.descriptionLower bounds estimates are proved for the first eigenvalue for the Dirichlet Laplacian on arbitrary triangles using various symmetrization techniques. These results can viewed as a generalization of Pólya's isoperimetric bounds. It is also shown that amongst triangles, the equilateral triangle minimizes the spectral gap and (under additional assumption) the ratio of the first two eigenvalues. This last result resembles the Payne-Pólya-Weinberger conjecture proved by Ashbaugh and Benguria.
dc.identifierhttps://arxiv.org/abs/0707.3631
dc.identifierhttp://arxiv.org/abs/0707.3631
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164981
dc.subjectSpectral Theory
dc.subject35P15
dc.titleIsoperimetric inequalities for eigenvalues of triangles
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