Course Title: Riemannian Geometry
Course
#: MAT 552
Day/Time: Monday, 5:00-7:00 p.m.
Location: Fine 1201
This semester we will continue with the
construction of harmonic maps and minimal surfaces in Riemannian manifolds for
the first part of the semester. Then we
will study conformal structures on Riemannian manifolds, starting with a
relatively rapid review of the Yamabe problem and recent progress.
We will then study the conformally compact
manifolds, covering some work of Graham-Fefferman, Anderson and Qing. The main topics are the definition of the
Paneitz operators as boundary operators of the conformal infinity, the notion
of renormalized volume and its relation to the Gauss-Bonnet integral. The question of existence and uniqueness of
the conformally compact Einstein manifold given the conformal structure of the
boundary will be discussed.
First Meeting: February 17, 2003