In the semiclassical limit, the transition ratio for optimal cuboid shapes in Robin Riesz means differs from the ratio where the second term in the eigenvalue asymptotics changes sign.
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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.
citing papers explorer
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Optimizing Riesz means of Robin Laplace operators on cuboids in a semiclassical limit
In the semiclassical limit, the transition ratio for optimal cuboid shapes in Robin Riesz means differs from the ratio where the second term in the eigenvalue asymptotics changes sign.
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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.