The spectrum of the Laplacian on forms.

@article{Charalambous2016TheSO,
  title={The spectrum of the Laplacian on forms.},
  author={Nelia Charalambous and Zhiqin Lu},
  journal={arXiv: Differential Geometry},
  year={2016}
}
In this article we prove a generalization of Weyl's criterion for the spectrum of a self-adjoint nonnegative operator on a Hilbert space. We will apply this new criterion in combination with Cheeger-Fukaya-Gromov and Cheeger-Colding theory to study the $k$-form essential spectrum over a complete manifold with vanishing curvature at infinity or asymptotically nonnegative Ricci curvature. In addition, we will apply the generalized Weyl criterion to study the variation of the spectrum of a self… 
2 Citations
The spectrum of the Laplacian on forms over flat manifolds
In this article we prove that the spectrum of the Laplacian on $k$-forms over a noncompact flat manifold is always a connected closed interval of the nonnegative real line. The proof is based on a

References

SHOWING 1-10 OF 33 REFERENCES
The spectrum of the Laplacian on a manifold of nonnegative Ricci curvature
The study of the spectrum of the Laplacian on a complete noncompact Riemannian manifold has received much attention during the past decade or so. In particular, it has been conjectured and partially
On the Lp-Spectrum of Uniformly Elliptic Operators on Riemannian Manifolds
Abstract We prove that the L p spectrum of uniformly elliptic divergence form operators on a complete Riemannian manifold is independent of p ∈ [1, ∞] if the volume of the manifold grows uniformly
On the spectrum of the Laplacian
In this article we prove a generalization of Weyl’s criterion for the essential spectrum of a self-adjoint operator on a Hilbert space. We then apply this criterion to the Laplacian on functions over
On the essential spectrum of complete non-compact manifolds☆
Spectral convergence under bounded Ricci curvature
Eigenvalues of the Laplacian on forms
Some bounds for eigenvalues of the Laplace operator acting on forms on a compact Riemannian manifold are derived. In case of manifolds without boundary we give upper bounds in terms of the curvature,
Periodic manifolds with spectral gaps
ON THE UPPER ESTIMATE OF THE HEAT KERNEL OF A COMPLETE RIEMANNIAN MANIFOLD
Let M be a complete non-compact Riemannian manifold whose sectional curvature is bounded between two constants -k and K. Then one expects that the heat diffusion in such a manifold behaves like the
Complete manifolds with bounded curvature and spectral gaps
...
...