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.
van den Berg,On the minimization of Dirichlet eigenvalues
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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.