We construct asymptotically Euclidean solutions of the vacuum Einstein
constraint equations with an apparent horizon boundary condition. Specifically,
we give sufficient conditions for the constant mean curvature conformal method
to generate such solutions. The method of proof is based on the barrier method
used by Isenberg for compact manifolds without boundary, suitably extended to
accommodate semilinear boundary conditions and low regularity metrics. As a
consequence of our results for manifolds with boundary, we also obtain
improvements to the theory of the constraint equations on asymptotically
Euclidean manifolds without boundary.Comment: 27 pages, 1 figure, TeX, v3. Final version to appear in CMP.
Exposition has been extensively tightened and the proof of Proposition 3.5
has been simplifie
