On the Strong Lp-Hodge decomposition over complete Riemannian manifolds

We establish the Strong Lp-Hodge decomposition theorem and the Lp-Poincaré inequalities on differential forms over complete non-compact Riemannian manifolds. As applications, we prove some Lp-estimates and existence theorems for the de Rham operator as well as some vanishing theorems for the Lp-cohomology and the Lp-torsion over complete non-compact Riemannian manifolds with suitable geometric conditions.