The Area of a Minimal Embedded 2 - Sphere in a Manifold Di ff eomorphic to S 3

The starting point of the proof of Theorem 1.1 is the well-known existence result proven by Smith [14] (see also an expository paper [7] and a new survey [4]). For any Riemannian manifold diffeomorphic to S, there exists an embedded minimal twodimensional sphere. The work of Smith was his Ph.D. thesis written under the direction of L. Simon. It relies on methods of the work of Pitts [13] and on results of Meeks, Simon, and Yau [9]. Note also that Jost proved that each Riemannian manifold diffeomorphic to