| We construct two new classes of solutions of the Einstein constraint equations. First, we construct a family of solutions on asymptotically Euclidean manifolds with boundary such that the boundary is an apparent horizon. This initial data has application to the general relativistic N-body problem. Second, we construct a family of low regularity asymptotically Euclidean solutions of the constraint equations. These solutions have a metric in Hsloc with s > 3/2 and are required for existence theorems for rough solutions of the Einstein evolution equations. In both cases, we adapt and extend the constant mean curvature conformal method to apply it to these new settings. |
