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research
Eigenvalues of the Laplacian on Riemannian manifolds
Authors
Qing-Ming Cheng
Xuerong Qi
Publication date
26 April 2011
Publisher
View
on
arXiv
Abstract
For a bounded domain
Ω
\Omega
Ω
with a piecewise smooth boundary in a complete Riemannian manifold
M
M
M
, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. By making use of a fact that eigenfunctions form an orthonormal basis of
L
2
(
Ω
)
L^2(\Omega)
L
2
(
Ω
)
in place of the Rayleigh-Ritz formula, we obtain inequalities for eigenvalues of the Laplacian. In particular, for lower order eigenvalues, our results extend the results of Chen and Cheng \cite{CC}.Comment: 17 page
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Last time updated on 30/10/2017