An asymptotic shape optimization problem for Riesz means of Laplacian eigenvalues
Spectral Theory
2026-04-21 v1 Mathematical Physics
math.MP
Abstract
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 definition of the Riesz means tends to infinity. We show that for a certain range of Riesz exponents, the optimizing sets converge to a ball. We also present some new results where we optimize over disjoint unions of convex sets.
Cite
@article{arxiv.2604.18262,
title = {An asymptotic shape optimization problem for Riesz means of Laplacian eigenvalues},
author = {Rupert L. Frank and Simon Larson},
journal= {arXiv preprint arXiv:2604.18262},
year = {2026}
}
Comments
The paper contains results that were contained in an earlier version of arXiv:2410.04769 but which did not appear in the final version