Vanishing Theorems for Conformally Compact Manifolds

Abstract

We study L ² harmonic p-forms on conformally compact manifolds with a rather weak boundary regularity assumption. We proved that if the lower bound of the curvature operator is great than or equal to ?1 and the infimum of the L ² spectrum of the Laplacian great than p(n ? p) for some p ≤ n/2, then there is no nontrivial L ² harmonic p-form.