L 2 Forms and Ricci Flow with Bounded Curvature on Complete Non-Compact Manifolds

摘要

In this paper, we study the evolution of L 2 one forms under Ricci flow with bounded curvature on a non-compact Rimennian manifold. We show on such a manifold that the L 2 norm of a smooth one form is non-increasing along the Ricci flow with bounded curvature. The L ∞ norm is showed to have monotonicity property too. Then we use L ∞ cohomology of one forms with compact support to study the singularity model for the Ricci flow on $S^1timesmathbb{R}^{n-1}$ .