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| Estimates for Eigenvalues of the Dirichlet Laplacian on Riemannian Manifolds |
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Citation： |
Daguang CHEN,Qing-Ming CHENG.Estimates for Eigenvalues of the Dirichlet Laplacian on Riemannian Manifolds[J].Chinese Annals of Mathematics B,2026,(1):169~184 |
| Page view： 191
Net amount： 98 |
Authors： |
Daguang CHEN; Qing-Ming CHENG |
Foundation： |
National Natural Science Foundation of China (No. 11831005, 1257010742), NSFC-FWO grant (No. 11961131001), JSPS Grant-in-Aid (No. 25K06992), MEXT Promotion..., Osaka Metropolitan University Strategic... |
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| Abstract： |
The authors revisit the eigenvalue problem of the Dirichlet Laplacian on bounded domains in complete Riemannian manifolds. They establish universal inequalities for eigenvalue gaps and Riesz means under various curvature assumptions. In particular, they refine Weyl’s asymptotic law by incorporating geometric corrections involving Ricci curvature and boundary mean curvature, providing sharper spectral estimates than previously known. |
Keywords： |
Laplacian Eigenvalues Weyl’s law Riesz mean Universal estimates |
Classification： |
53C42, 58J50 |
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