Program
Introduction to Geometric Analysis
Student No.:40
Time:Tue & Thu 09:50-11:25
Instructor:王丽涵 Wang Lihan  
Place:Conference Room 3, Jin Chun Yuan West Bldg.
Starting Date:2018-7-3
Ending Date:2018-7-31

The main goal of this course is to present some basic tools which are necessary for research in geometric analysis. We will start with some review on Riemannian geometry, like variational formulas for areas, volume comparison theorems and Bochner-Weitzenbock formula. Then we will discuss the Laplace equations, like the comparison theorems, first eigenvalue’s estimates and Gradient estimates. Further more, we will discuss the parabolicity. That is, how the Ricci lower bounds and the first eigenvalue imply the metric of manifolds. Another topic will be heat kernel, like the well-known Li-Yau estimate.


Prerequisite:Introduction to Riemannian geometry; second order elliptic PDE.


Reference:

"Geometric Analysis" by Peter Li, Cambridge studies in advanced mathematics.