Comparison of Laplace Beltrami Operator Eigenvalues on Riemannian Manifolds
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Let $\Delta_{g}$ be the Laplace Beltrami operator on a manifold $M$ with Dirichlet (resp.,
Neumann) boundary conditions. We compare the spectrum of on a Riemannian manifold
for Neumann boundary condition and Dirichlet boundary condition . Then we construct an
effective method of obtaining small eigenvalues for Neumann's problem.
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