Limit equation for vacuum Einstein constraints with a translational   Killing vector field in the compact hyperbolic case
  We construct solutions to the constraint equations in general relativity using the limit equation criterion introduced by Dahl, Humbert and the first author. We focus on solutions over compact 3-manifolds admitting a $\bS^1$-symmetry group. When the quotient manifold has genus greater than 2, we obtain strong far from CMC results. 
Romain Gicquaud and Cecile Huneau
gr-qc math.AP math.DG