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# Communications in Analysis and Geometry

## Volume 19 (2011)

### Number 5

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

Pages: 855 – 885

DOI: http://dx.doi.org/10.4310/CAG.2011.v19.n5.a2

#### Authors

#### Abstract

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.