Pinching estimates for solutions of the linearized Ricci flow system in higher dimensions

摘要

We prove pinching estimates for solutions of the linearized Ricci flow system on a closed manifold of dimension n >= 4 with positive scalar curvature and vanishing Weyl tensor. If the vanishing Weyl tensor condition is removed, we only give a rough pinching estimate controlled by some blow-up function in a short time. These results extend the 3-dimensional case due to Anderson and Chow (2005) [1]. (C) 2016 Elsevier B.V. All rights reserved.