On the absolutely continuous spectrum of the Laplace-Beltrami operator acting on p-forms for a class of warped product metrics

Abstract

We explicitely compute the absolutely continuous spectrum of the Laplace-Beltrami operator for $p$-forms for the class of warped product metrics $d\sigma^2= y^{2a}dy^2 + y^{2b}d\theta_{\Sphere^{N-1}}^2$, where $y$ is a boundary defining function on the unit ball B(0,1) in $\Real^N$.