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<p>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.</p>

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Sum rules and sharp eigenvalue bounds for compact homogeneous irreducible Riemannian manifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月22日

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  • Luigi Provenzano,
  • Joachim Stubbe

摘要

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.