A note on \(p\)-harmonic \(l\)-forms on complete manifolds (Q418435)

Take any complete noncompact Riemannian manifold \(M\) whose curvature operator is asymptotically nonnegative. For any numbers \(p > 1\) and \(q > 0\) and any set of \(p\)-harmonic differential forms of degree at least 1 bounded in \(L^q\)-norm, the authors prove that this set is relatively compact in the topology of uniform convergence. They make use of a new Bochner-type formula to prove their result.