%0 Journal Article
%T Neumann eigenvalue sums on triangles are (mostly) minimal for equilaterals
%A R. S. Laugesen
%A Z. C. Pan
%A S. S. Son
%J Mathematics
%D 2011
%I arXiv
%X We prove that among all triangles of given diameter, the equilateral triangle minimizes the sum of the first $n$ eigenvalues of the Neumann Laplacian, when $n \geq 3$. The result fails for $n=2$, because the second eigenvalue is known to be minimal for the degenerate acute isosceles triangle (rather than for the equilateral) while the first eigenvalue is 0 for every triangle. We show the third eigenvalue is minimal for the equilateral triangle.
%U http://arxiv.org/abs/1102.0071v1