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Spectral Gaps on Riemannian Manifolds

Helton Leal (Bellevue College)
Wednesday, April 21, 2021 - 4:00pm to 5:00pm

We survey some basic results related to the new Weyl criterion for the essential spectrum of the Laplacian on Riemannian manifolds. We then use the language of Gromov-Hausdorff convergence to prove a spectral gap theorem.  Finally, we make the necessary adjustments to extend our main results and construct a class of complete noncompact manifolds with an arbitrarily large number of gaps in the spectrum of the Hodge Laplacian acting on differential forms.

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