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

Andrzej Siudeja Bartłomiej (Department of Mathematics, University of Oregon)

Richard Snyder Laugesen (Department of Mathematics, University of Illinois at Urbana)

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.

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