  We show how to reduce the general formulation of the mass-angular momentum
inequality, for axisymmetric initial data of the Einstein equations, to the
known maximal case whenever a geometrically motivated system of equations
admits a solution. This procedure is based on a certain deformation of the
initial data which preserves the relevant geometry, while achieving the maximal
condition and its implied inequality (in a weak sense) for the scalar
curvature; this answers a question posed by R. Schoen. The primary equation
involved, bears a strong resemblance to the Jang-type equations studied in the
context of the positive mass theorem and the Penrose inequality. Each equation
in the system is analyzed in detail individually, and it is shown that
appropriate existence/uniqueness results hold with the solution satisfying
desired asymptotics. Lastly, it is shown that the same reduction argument
applies to the basic inequality yielding a lower bound for the area of black
holes in terms of mass and angular momentum.
