Let g and g be Riemannian metrics on a noncompact manifold M, which are conformally equivalent. We show that under a very mild first order control on the conformal factor, the wave operators corresponding to the Hodge-Laplacians Δg and Δg acting on differential forms exist and are complete. We apply this result to Riemannian manifolds with bounded geometry and more specifically, to warped product Riemannian manifolds with bounded geometry. Finally, we combine our results with some explicit calculations by Antoci to determine the absolutely continuous spectrum of the Hodge-Laplacian on j-forms for a large class of warped product metrics.

Scattering theory of the Hodge-Laplacian under a conformal perturbation / Bei, F; Guneysu, B.; Muller, J.. - In: JOURNAL OF SPECTRAL THEORY. - ISSN 1664-039X. - 7:1(2017), pp. 235-267. [10.4171/JST/162]

Scattering theory of the Hodge-Laplacian under a conformal perturbation

Bei F
;
2017

Abstract

Let g and g be Riemannian metrics on a noncompact manifold M, which are conformally equivalent. We show that under a very mild first order control on the conformal factor, the wave operators corresponding to the Hodge-Laplacians Δg and Δg acting on differential forms exist and are complete. We apply this result to Riemannian manifolds with bounded geometry and more specifically, to warped product Riemannian manifolds with bounded geometry. Finally, we combine our results with some explicit calculations by Antoci to determine the absolutely continuous spectrum of the Hodge-Laplacian on j-forms for a large class of warped product metrics.
2017
Conformal perturbations; Hodge-Laplacian; Scattering theory; Wave operators
01 Pubblicazione su rivista::01a Articolo in rivista
Scattering theory of the Hodge-Laplacian under a conformal perturbation / Bei, F; Guneysu, B.; Muller, J.. - In: JOURNAL OF SPECTRAL THEORY. - ISSN 1664-039X. - 7:1(2017), pp. 235-267. [10.4171/JST/162]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1362794
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