In this paper, we study the evolution of L 2 p-forms under Ricci flow with bounded curvature on a complete noncompact or a compact Riemannian manifold. We show that under the curvature operator bound condition on such a manifold, the weighted L 2 norm of a smooth p-form is non-increasing along the Ricci flow. The weighted L∞ norm is showed to have monotonicity property too.
Liu, Baiyu and Ma, Li, "L2p-Forms and Ricci Flow with Bounded Curvature on Manifolds" (2009). ICEB 2009 Proceedings (Macau, SAR China). 139.