Let (M m , g) be a complete non-compact manifold with asymptotically non-negative Ricci curvature and finite first Betti number. We prove that any bounded set of p-harmonic 1-forms in L q (M ), 0 < q < ∞, is relatively compact with respect to the uniform convergence topology. Mathematics Subject Classification (2000). 58A10, 53C21.

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.