Abstract
For a bounded domain in a complete Riemannian manifold isometrically immersed in a Euclidean space, we derive extrinsic estimates for eigenvalues of the Dirichlet eigenvalue problem of the Laplace operator, which depend on the mean curvature of the immersion. Further, we also obtain an upper bound for the eigenvalue, which is best possible in the meaning of order on .
Citation
Daguang CHEN. Qing-Ming CHENG. "Extrinsic estimates for eigenvalues of the Laplace operator." J. Math. Soc. Japan 60 (2) 325 - 339, April, 2008. https://doi.org/10.2969/jmsj/06020325
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