## Inequalities for eigenvalues of the biharmonic operator with weight on Riemannian manifolds.(English)Zbl 1200.53042

Given a compact Riemannian manifold with boundary, the authors consider the eigenvalues of the biharmonic operator with weight on $$M$$. They prove a general inequality involving these eigenvalues. Using this inequality, they consider these eigenvalues when $$M$$ is a compact domain of the following three space: 1) a complex projective space, 2) a minimal submanifold of a Euclidean space and 3) a minimal submanifold of a unit sphere.

### MSC:

 53C20 Global Riemannian geometry, including pinching 58C40 Spectral theory; eigenvalue problems on manifolds 35P15 Estimates of eigenvalues in context of PDEs 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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### References:

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