Comparison of Laplace Beltrami Operator Eigenvalues on Riemannian Manifolds



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Submitted Aug 7, 2022
Published Oct 23, 2022
10.24018/ejmath.2022.3.5.143

Abstract viewed = 133 times

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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.

 

Keywords: Eigenvalue problem, Laplacian, manifold, spectrum

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