Some Topics in the Ricci Flow

Abstract

The Ricci flow plays an essential role in modern geometric analysis. In this short note, we only survey some special topics of this broad and deep field. We first survey some convergence results of the Ricci flow and the Kähler Ricci flow. In particular, we explain the basic idea in the proof of the Hamilton-Tian conjecture. Then we survey the recent progresses on the extension conjecture, which predicts that the Ricci flow can be extended when scalar curvature is bounded.