  We present a 2+1 decomposition of the vacuum initial conditions in general
relativity. For a constant mean curvature one of the momentum constraints
decouples in quasi isotropic coordinates and it can be solved by quadrature.
The remaining momentum constraints are written in the form of the tangential
Cauchy-Riemann equation. Under additional assumptions its solutions can be
written in terms of integrals of known functions. We show how to obtain initial
data with a marginally outer trapped surface. A generalization of the Kerr data
is presented.
