Richard Schoen

The Yamabe Problem: An Interaction between Relativity and Geometry

In this lecture we will discuss the geometric question of construction of Riemannian metrics of constant scalar curvature. This problem turns out to have an intimate connection with gravitational mass in relativity. We will discuss this connection and survey the recent activity on the Yamabe problem which has provided a much more thorough understanding of constant scalar curvature metrics both from a variational and heat equation point of view.