A note onp-harmonicl-forms on complete manifolds

Abstract

Let (M m , g) be an m-dimensional complete noncompact manifold. We show that for all p > 1 and l > 1, any bounded set of p-harmonic l-forms in L q (M), with 0 < q < ∞, is relatively compact with respect to the uniform convergence topology if the curvature operator of M is asymptotically nonnegative.