On the Strong [formula omitted]-Hodge decomposition over complete Riemannian manifolds

Abstract

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