J. Isenberg et V. Moncrief, A SET OF NONCONSTANT MEAN-CURVATURE SOLUTIONS OF THE EINSTEIN CONSTRAINT EQUATIONS ON CLOSED MANIFOLDS, Classical and quantum gravity, 13(7), 1996, pp. 1819-1847
We prove that a certain class of conformal data (open in the set of al
l conformal data) maps to solutions of the Einstein constraint equatio
ns with nonconstant mean curvature. The method of proof is constructiv
e, and it should apply to larger classes of conformal data as well.