Quasi-spherical metrics and prescribed scalar curvature

We describe a construction for metrics of prescribed scalar curvature on S 2 xR, based on a quasi-spherical coordinate condition.The construction uses two arbitrary functions and requires the solution of a semilinear parabolic equation on S , with the arbitrary functions and the scalar curvature appearing as source terms.We obtain existence results for this equation under various geometrically natural boundary conditions, and thereby construct some 3-metrics of interest in general relativity.