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math.SP2026
Robin counting functions on cuboids in the critical scaling regime
Matthias Baur, Simon Larson
We consider eigenvalue counting functions of Robin Laplace operators on cuboids where the Robin parameter and the spectral cut-off are coupled. Our main focus is the critical r…
math.SP2026
An asymptotic shape optimization problem for Riesz means of Laplacian eigenvalues
Rupert L. Frank, Simon Larson
We review our recent results on the problem of optimizing Riesz means of Laplace eigenvalues among convex sets of given measure in the regime where the cut-off parameter in the def…
math.SP2026
Optimizing Riesz means of Robin Laplace operators on cuboids in a semiclassical limit
Matthias Baur, Simon Larson
We study asymptotic shape optimization for Riesz means of Robin Laplacian eigenvalues among cuboids of fixed measure. Our focus is the regime where the Robin parameter is proportio…