arXiv 1102.00712011-02-01math.APmath-phmath.MP

Neumann eigenvalue sums on triangles are (mostly) minimal for equilaterals

R. S. Laugesen, Z. C. Pan, S. S. Son

备注：: 12 pages, 2 figures, 2 tables

英文摘要：

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.

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