Shubham Swivedi, Department of Pure Mathematics, University of Waterloo
“Yamabe Problem and Conformal Geometry”
We will complete Section 4 of the Lee/Parker paper. We will show that the Yamabe Problem can be solved for the Sphere by using Uhlenbeck’s ”Renormalisation” approach. If time permits, then we will discuss some Conformal Geometry and use it to give a proof of a theorem of Aubin that if a compact Riemannian manifold has dimension greater than or equal to 6 and is not locally conformally flat then the Yamabe invariant of the manifold is strictly less than the Yamabe Invariant of the Sphere.