%0 Journal Article
%T A Reilly formula and eigenvalue estimates for differential forms
%A Simon Raulot
%A Alessandro Savo
%J Mathematics
%D 2010
%I arXiv
%R 10.1007/s12220-010-9161-0
%X 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 by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.
%U http://arxiv.org/abs/1003.0817v1