  We derive a positive mass theorem for asymptotically flat manifolds with
boundary whose mean curvature satisfies a sharp estimate involving the
conformal Green's function. The theorem also holds if the conformal Green's
function is replaced by the standard Green's function for the Laplacian
operator. As an application, we obtain an inequality relating the mass and
harmonic functions that generalizes H. Bray's mass-capacity inequality in his
proof of the Riemannian Penrose conjecture.
