Part I:

In 1960 H. Yamabe conjectured that given a compact Riemannian manifold, there exists a conformal deformation of the metric to one of constant scalar curvature. The combined works of Yamabe, N. Trudinger, T. Aubin, and R. Schoen gave an affirmative solution in 1984. In this talk we review Yamabe's original paper and give the proof of Yamabe's conjecture in the case when the Yamabe energy is nonpositive.

Part II:

In 1960 H. Yamabe conjectured that given a compact Riemannian manifold, there exists a conformal deformation of the metric to one of constant scalar curvature. In this tal…