Ricci flow deforms the Riemannian structure of a manifold in the direction of its Ricci curvature and tends to regularize the metric. Ricci solitons are special solutions to the Ricci flow and arise naturally in the singularity analysis of the flow. We shall talk about some curvature and entropy gap theorems of gradient Ricci solitons. In the second part of the talk, we shall discuss an optimal gap theorem on nonnegatively curved manifolds with small average curvature decay. This talk is based on joint works with Zilu Ma and Yongjia Zhang, and Man-Chun Lee.
 

PS: This is a joint analysis seminar and nonlinear PDEs seminar