Geometric Analysis Working Seminar

Shubham Dwivedi, Department of Pure Mathematics, University of Waterloo

“Mass of Asymptotically flat manifolds.”

We will start with Section 7 of the Lee/Parker paper on the Yamabe Problem. After a brief review of the problem and techniques developed so far, we will define the ”mass” of an asymptotically flat manifold. We will show that the relationship between the Yamabe invariant of a compact Riemannian manifold and that of the Sphere depends on the ”mass” of the manifold. The solution to the Yamabe Problem (in cases when dimension of the manifold is 3, 4 or 5 or if the manifold is locally conformally flat) then follows from the Positive Mass Theorem, as proved by Schoen and Yau, and also by Witten.

MC 5403