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In this short article, we explore some basic results associated to the Generalized Weyl criterion for the essential spectrum of the Laplacian on Riemannian manifolds. We use the language of Gromov-Hausdorff convergence to recall 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.more » « less
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In this short article, we explore some basic results associated to the Generalized Weyl criterion for the essential spectrum of the Laplacian on Riemannian manifolds. We use the language of Gromov-Hausdorff convergence to recall 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.more » « less
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In this paper, we generalize the spectrum relation in the paper "On the spectrum of the Laplacian, Math. Ann., 359(1-2):211--238, 2014, by Nelia Charalambous and Zhiqin Lu" to any Hermitian manifolds. We also prove that the closure of the Laplace operator on the moduli space of polarized Calabi-Yau manifolds is self-adjoint.more » « less
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