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

Mathematics – Spectral Theory

Scientific paper

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45 pages, to appear in "Advances in Mathematics"

Scientific paper

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

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