Canonical Metrics in Differential Geometry
The canonical metrics play an important role in the investigation of geometry and topology of a manifold. The existence of canonical metrics is associated to the study of certain partial differential equations arising from geometry. The course will focus on the existence of Kahler-Einstein metrics on a compact complex manifold with a definite sign of the first Chern class, both elliptic arguments and parabolic arguments will be provided. We will also talk about Hamilton’s work on Ricci flow on compact manifolds in dimension 2, 3, 4.
One semester courses of complex geometry, Riemannian geometry and partial differential equations.