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<p>The authors revisit the eigenvalue problem of the Dirichlet Laplacian on bounded domains in complete Riemannian manifolds. By building on classical results like Li-Yau’s and Yang’s inequalities, they derive upper and lower bounds for eigenvalues. For the projective spaces and their minimal submanifolds, they also give explicit estimates on the lower bound for the eigenvalue of the Dirichlet Laplacian.</p>

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Estimates for Eigenvalues of the Dirichlet Laplacian on Riemannian Manifolds

  • 期刊论文

  • 发表日期：

    2025年12月17日

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  • Daguang Chen,
  • Qing-Ming Cheng

摘要

The authors revisit the eigenvalue problem of the Dirichlet Laplacian on bounded domains in complete Riemannian manifolds. By building on classical results like Li-Yau’s and Yang’s inequalities, they derive upper and lower bounds for eigenvalues. For the projective spaces and their minimal submanifolds, they also give explicit estimates on the lower bound for the eigenvalue of the Dirichlet Laplacian.