  In this short note, we give a construction of solutions to the Einstein
constraint equations using the well known conformal method. Our method gives a
result similar to the one in [15, 16, 24], namely existence when the so called
TT-tensor $\sigma$ is small and the Yamabe invariant of the manifold is
positive. The method we describe is however much simpler than the original
method and allows easy extensions to several other problems. Some non-existence
results are also considered.
