A Reilly Formula and Eigenvalue Estimates for Differential Forms

  title={A Reilly Formula and Eigenvalue Estimates for Differential Forms},
  author={Simon Raulot and Alessandro Savo},
  journal={Journal of Geometric Analysis},
  • S. Raulot, A. Savo
  • Published 3 March 2010
  • Mathematics
  • Journal of Geometric Analysis
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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Einstein manifolds
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