Shubham Dwivedi, Department of Pure Mathematics, University of Waterloo
“The Green’s function and asymptotically flat manifolds”
We will begin Section 6 of the Lee/Parker paper. We start by generalizing the notion of stereographic projection to any compact Riemannian manifold with strictly positive Yamabe invariant and subsequently define asymptotically flat manifolds. We then prove the existence of a Green’s function for the operator in the Yamabe equation, at every point of the manifold, if the Yamabe invariant is positive. If time permits, using conformal normal coordinates, we will see the asymptotic expansion of the Green’s function and as an application of this we will give an explicit description of the generalized stereographic projection.