MATH 6140 - Introduction to the Ricci Flow (topics in analysis)

Xiadong Cao, spring 2014

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. Some other useful technique will also be discussed. Finally, Perelman's entropy functional will be discussed at the end. This course aims at second and third year graduate students who has some background in differential geometry and partial differential equations.