Dirichlet eigenvalue sums on triangles are minimal for equilaterals

作者：Laugesen Richard Snyder^*; Siudeja Bartlomiej Andrzej

来源：Communications in Analysis and Geometry, 2011, 19(5): 855-885.

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 >= 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.

• 出版日期2011-12