A non-existence result for a generalization of the equations of the   conformal method in general relativity
  The constraint equations of general relativity can in many cases be solved by the conformal method. We show that a slight modification of the equations of the conformal method admits no solution for a broad range of parameters. This suggests that the question of existence or non-existence of solutions to the original equations is more subtle than could perhaps be expected. 
Mattias Dahl, Romain Gicquaud, Emmanuel Humbert
gr-qc math.AP math.DG