Dirichlet eigenvalue sums on triangles are minimal for equilaterals

Richard Laugesen; Bartlomiej Siudeja

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arXiv · 1008.1316

Dirichlet eigenvalue sums on triangles are minimal for equilaterals

Richard Laugesen·Bartlomiej Siudeja

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Abstract

Among all triangles of given diameter, the equilateral triangle is shown to minimize the sum of the first $n$ eigenvalues of the Dirichlet Laplacian, for each $n \geq 1$. In addition, the first, second and third eigenvalues are each proved to be minimal for the equilateral triangle. The disk is conjectured to be the minimizer among general domains.

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BibTeX RIS

Richard Laugesen, Bartlomiej Siudeja. 2010-08-07. Dirichlet eigenvalue sums on triangles are minimal for equilaterals. https://arxiv.org/abs/1008.1316

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