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Abstract 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 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.
Branding et al. (Sun,) studied this question.