Sum rules and sharp eigenvalue bounds for compact homogeneous irreducible Riemannian manifolds
Luigi Provenzano, Joachim Stubbe · Annals of Global Analysis and Geometry · 2025
Abstract We exploit an identity for the gradients of Laplacian eigenfunctions on compact homogeneous Riemannian manifolds with irreducible linear isotropy group to obtain asymptotically sharp universal eigenvalue inequalities and sharp Weyl bounds on Riesz means. The approach is non variational and is based on identities for spectral quantities in the form of sum rules.