Volker Branding, Georges Habib
Published 2022-01-17, updated 2022-03-22Version 2
We derive various eigenvalue estimates for the Hodge Laplacian acting on differential forms on weighted Riemannian manifolds. Our estimates unify and extend various results from the literature and we provide a number of geometric applications. In particular, we derive an inequality which relates the eigenvalues of the Jacobi operator for (f)-minimal hypersurfaces and the spectrum of the Hodge Laplacian.
Some Isoperimetric Inequalities and Eigenvalue Estimates in Weighted Manifolds
Eigenvalue estimates for 3-Sasaki structures
Spectrum of the Laplacian and the Jacobi operator on rotational cmc hypersurfaces of spheres
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