## Eigenvalue relationships between Laplacians of constant mean curvature hypersurfaces in $$\mathbb{S}^{n+1}$$.(English)Zbl 1275.58016

Summary: For compact hypersurfaces with constant mean curvature in the unit sphere, we give a comparison theorem between eigenvalues of the stability operator and that of the Hodge Laplacian on 1-forms. Furthermore, we also establish a comparison theorem between eigenvalues of the stability operator and that of the rough Laplacian.

### MSC:

 58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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### References:

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