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This is a Quantitative Study study.

October 20, 2025Open Access

Semiclassical eigenvalue bounds for compact homogeneous irreducible Riemannian manifolds

Key Points

The study establishes asymptotically sharp eigenvalue inequalities for Riemannian manifolds with irreducible isotropy.
Eigenfunctions of the Laplacian are analyzed, resulting in sharp Weyl bounds on Riesz means.
A non-variational approach is implemented, utilizing identities for spectral quantities in the form of sum rules.
This research enhances understanding of spectral behavior on these complex geometrical structures.

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.

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Provenzano et al. (Tue,) studied this question.

synapsesocial.com/papers/68f5fcce8d54a28a75cf1ac6 — DOI: https://doi.org/10.48550/arxiv.2503.02716

Authors

Luigi Provenzano

Sapienza University of Rome

Joachim Stubbe

École Polytechnique Fédérale de Lausanne

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Semiclassical eigenvalue bounds for compact homogeneous irreducible Riemannian manifolds

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Abstract

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Authors

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