A Note on p-Harmonic $$\ell $$-Forms on Complete Non-compact Manifolds

Vanishing Theorems for p-Harmonic Forms on Submanifolds in Spheres

“…Next, we will give some important lemmas. Lemma 2.2 [15] For p ≥ 2 and ≥ 1, let be a p-harmonic ℓ-form on an n-dimensional complete Riemannian manifold M. Then…”