Communications in Analysis and Geometry
Volume 19 (2011)
Dirichlet eigenvalue sums on triangles are minimal for equilaterals
Pages: 855 – 885
Among all triangles of given diameter, the equilateraltriangle is shown to minimize the sum of the first $n$eigenvalues of the Dirichlet Laplacian, for each $n \geq1$. In addition, the first, second and third eigenvaluesare each proved to be minimal for the equilateral triangle.
The disk is conjectured to be the minimizer among general domains.