Cornell Math - MATH 711, Fall 2006

MATH 711: Seminar in Analysis (Fall 2006)

Instructor: Xiaodong Cao

Meeting Time & Room

In this course, we will give an introduction to the Ricci flow. First we will give a brief review to Riemannian geometry. We will start the study of the Ricci flow with considering special solutions to the Ricci flow. We will talk about the short time existence, maximal principle, Li-Yau-Hamilton type differential Harnack inequality and derivative estimates. We will give a comprehensive treatment of the Ricci flow on surfaces. We will also study Hamilton's original paper on three-manifolds with positive Ricci curvature. Finally, Perelman's entropy functional will be discussed at the end.