On Hamilton's Ricci flow and Bartnik's construction of metrics of prescribed scalar curvature

It is known by work of R. Hamilton and B. Chow that the evolution under Ricci flow of an arbitrary initial metric g on S 2, suitably normalized, exists for all time and converges to a round metric. I construct metrics of prescribed scalar curvature using solutions to the Ricci flow. The problem is converted into a semilinear parabolic equation similar to the quasispherical construction of Bartnik. In this work, I discuss existence results for this equation and applications of such metrics.