Riemannian manifolds whose Laplacians have purely continuous spectrum.
Harold Donnelly, Nicola Garafalo (1992)
Mathematische Annalen
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Harold Donnelly, Nicola Garafalo (1992)
Mathematische Annalen
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Regina Kleine (1988)
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Katsumi Nomizu, Kentaro Yano (1967)
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M. Glasner, R. Katz, M. Nakai (1971)
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Oldrich Kowalski (1974)
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Xiao-Wie Peng (1989)
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Georgi S. Popov (1993)
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Gudlaugur Thorbergsson (1978)
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Grigorios Tsagas (1978/79)
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Robert Brooks (1984)
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Carolyn S. Gordon, Juan Pablo Rossetti (2003)
Annales de l'Institut Fourier
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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...
Norio Ejiri (1979)
Mathematische Zeitschrift
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