An application of scattering theory to the spectrum of the Laplace-Beltrami operator

Applying a theorem due to Belopol’ski and Birman, we show that the Laplace-Beltrami operator on 1-forms on ${\mathbf{R}}^n$ endowed with an asymptotically Euclidean metric has absolutely continuous spectrum equal to $[0,+\mathrm{\infty })$.