Dirichlet eigenvalue sums on triangles are minimal for equilaterals

Details Dirichlet eigenvalue sums on triangles are minimal for equilaterals Dirichlet eigenvalue sums on triangles are minimal for equilaterals

2010-08-07

arxiv.org/abs/1008.1316v1

Mathematics

Spectral Theory

Scientific paper

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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