Chih-Wei Chen
Published 2016-02-05Version 1
We show that a uniform local bound for the curvature operator can be derived from local bounds of Ricci curvature and injectivity radius among all $n$-dimensional Ricci flows. As a consequence, we obtain new compactness theorems for the Ricci flow and Ricci soliton without assuming any bounds on the curvature operator. In the second part of this paper, we discuss the behavior of Ricci curvature and its derivative when the injectivity radius is thoroughly unknown. In particular, a Shi-type estimate for Ricci curvature is derived when the derivative of Ricci curvature is controlled by the derivative of scalar curvature.
The ultimate upper bound on the injectivity radius of the Stiefel manifold
On the injectivity radius and tangent cones at infinity of gradient Ricci solitons
Ricci curvature and monopole classes on 3-manifolds
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