A Reilly formula and eigenvalue estimates for differential forms
Abstract
We derive a Reillytype formula for differential pforms 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 nonnegatively curved. Finally we also obtain, as a byproduct of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports nontrivial parallel forms.
 Publication:

arXiv eprints
 Pub Date:
 March 2010
 arXiv:
 arXiv:1003.0817
 Bibcode:
 2010arXiv1003.0817R
 Keywords:

 Mathematics  Differential Geometry;
 58J50;
 58J32;
 53C24
 EPrint:
 22 pages