A Reilly formula and eigenvalue estimates for differential forms
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2010
- DOI:
- 10.48550/arXiv.1003.0817
- arXiv:
- arXiv:1003.0817
- Bibcode:
- 2010arXiv1003.0817R
- Keywords:
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- Mathematics - Differential Geometry;
- 58J50;
- 58J32;
- 53C24
- E-Print:
- 22 pages