Scattering theory of the Hodge-Laplacian under a conformal perturbation

Francesco Bei, Batu Güneysu, Jörn Müller

Published 2014-07-02, updated 2014-10-01Version 2

Let $g$ and $\tilde{g}$ be Riemannian metrics on a noncompact manifold $M$, which are conformally equivalent. We show that under a very mild \emph{first order} control on the conformal factor, the wave operators corresponding the Hodge-Laplacian $\Delta_g$ and $\Delta_{\tilde{g}}$ acting on differential forms exist and are complete.