QUASI-SPHERICAL METRICS AND PRESCRIBED SCALAR CURVATURE

We describe a construction for metrics of prescribed scalar curvature on S2 x R, based on a quasi-spherical coordinate condition. The construction uses two arbitrary functions and requires the solution of a semilinear parabolic equation on S2, 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.