L2p-Forms and Ricci Flow with Bounded Curvature on Manifolds

Authors

Baiyu Liu, Department of Mathematical Sciences, Tsinghua University, Beijing 100084, ChinaFollow
Li Ma, Department of Mathematical Sciences, Tsinghua University, Beijing 100084, ChinaFollow

Document Type

Article

Abstract

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.

Recommended Citation

Liu, Baiyu and Ma, Li, "L2p-Forms and Ricci Flow with Bounded Curvature on Manifolds" (2009). ICEB 2009 Proceedings (Macau, SAR China). 139.
https://aisel.aisnet.org/iceb2009/139