Riemannian manifolds whose Laplacians have purely continuous spectrum.
Harold Donnelly, Nicola Garafalo (1992)
Mathematische Annalen
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Displaying similar documents to “Spectral Geometry for Certain Noncompact Riemannian Manifolds.”
Riemannian manifolds whose Laplacians have purely continuous spectrum.
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Let be a -dimensional compact Riemannian manifold. We show that the spectrum of the Hodge Laplacian acting on -forms does not determine whether the manifold has boundary, nor does it determine the lengths of the closed geodesics. Among the many examples are a projective space and a hemisphere that have the same Hodge spectrum on 1- forms, and hyperbolic surfaces, mutually isospectral on 1-forms, with different injectivity radii. The Hodge -spectrum also does not distinguish orbifolds...
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