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• W2783239937 abstract "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-adjoint operator under continuous perturbations of the operator. In the particular case of the Laplacian on $k$-forms over a complete manifold we will use these analytic tools to find significantly stronger results for its spectrum including its behavior under a continuous deformation of the metric of the manifold." @default.
• W2783239937 created "2018-01-26" @default.
• W2783239937 creator A5068892304 @default.
• W2783239937 creator A5077342926 @default.
• W2783239937 date "2018-01-09" @default.
• W2783239937 modified "2023-10-16" @default.
• W2783239937 title "The spectrum of the Laplacian on forms" @default.
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• W2783239937 doi "https://doi.org/10.48550/arxiv.1801.02952" @default.
• W2783239937 hasPublicationYear "2018" @default.
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