Some Topics in the Ricci Flow (Journal of Mathematical Study, 2024)
The Ricci flow plays an essential role in modern geometric analysis. In thisshort note, we only survey some special topics of this broad and deep field. We firstsurvey 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 wesurvey the recent progresses on the extension conjecture, which predicts that the Ricciflow can be extended when scalar curvature is bounded.
Keywords: Ricci flow; Kähler Ricci flow; Hamilton-Tian conjecture; scalar curvature; extension problem.