  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.

Differential Geometry