On the spectrum of the Laplace-Beltrami operator for $p$-forms for a class of warped product metrics

Abstract

We explicitely compute the essential spectrum of the Laplace-Beltrami operator for $p$-forms for the class of warped product metrics $d{\sigma }^2=y^{2a}d{y}^2+y^{2b}d{\theta }_{\partial M}^2$, where $y$ is a boundary defining function on a compact manifold with boundary $M$.

45 pages, to appear in "Advances in Mathematics"

References in corpus (1)

• On the spectrum of the Laplace-Beltrami operator for p-forms on asymptotically hyperbolic manifolds