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Scattering theory for the Hodge-Laplacian


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Keywords :
Scattering theory, Wave operators; Bismut type derivative formulae; Hodge-Laplacian
Abstract :
[en] We prove using an integral criterion the existence and completeness of the wave operators corresponding to the Hodge-Laplacians acting on differential p-forms, induced by two quasi-isometric Riemannian metrics g and h on a complete open smooth manifold M. In particular, this result provides a criterion for the absolutely continuous spectra to coincide. The proof is based on gradient estimates obtained by probabilistic Bismut-type formulae for the heat semigroup defined by spectral calculus. By these localised formulae, the integral criterion only requires local curvature bounds and some upper local control on the heat kernel acting on functions, but no control on the injectivity radii. A consequence is a stability result of the absolutely continuous spectrum under a Ricci flow. As an application we concentrate on the important case of conformal perturbations.
Disciplines :
Author, co-author :
BAUMGARTH, Robert ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
Title :
Scattering theory for the Hodge-Laplacian
Alternative titles :
[en] Scattering theory for the Hodge-Laplacian
[de] Zur Streutheorie des Hodge-de Rham Laplace-Operators
[fr] Sur la théorie dispersion du laplacien de Hodge-de Rham
Publication date :
July 2020
Number of pages :
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since 27 July 2020


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