For a range of Riesz exponents, optimizers of Riesz means of Laplacian eigenvalues among convex sets of given measure converge to the ball in the high-cutoff limit.
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An asymptotic shape optimization problem for Riesz means of Laplacian eigenvalues
For a range of Riesz exponents, optimizers of Riesz means of Laplacian eigenvalues among convex sets of given measure converge to the ball in the high-cutoff limit.