MATH 7610: Riemannian Geometry and Geometric Analysis (Fall 2012)

Instructor: Xiaodong Cao

Textbook:Lectures on Differential Geometry by Schoen and Yau.

This topic course will be a continuation of MATH 6620. We will cover the following topics: comparison theorems and gradient estimates, harmonic functions on manifolds with negative curvature, eigenvalue problems, heat kernel on Riemannian manifolds, conformal deformation of scalar curvatures, etc. We will also discuss geometric flows if possible.