ON THE $L^2$ FORM SPECTRUM OF THE LAPLACIAN ON NONNEGATIVELY CURVED MANIFOLDS

Abstract

Let $(M,g_o)$ be a complete, noncompact Riemannian manifold with a pole, and let $g=fg_o$ be a conformally related metric. We obtain conditions on the curvature of $g_o$ and on $f$ under which the Laplacian on $p$-forms on $(M,g)$ has no eigenvalues.