# A Reilly Formula and Eigenvalue Estimates for Differential Forms

@article{Raulot2011ARF, title={A Reilly Formula and Eigenvalue Estimates for Differential Forms}, author={Simon Raulot and Alessandro Savo}, journal={Journal of Geometric Analysis}, year={2011}, volume={21}, pages={620-640} }

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally, we also obtain, as a byproduct of our calculations, an…

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