  A C^2 function on C^n is called (n-1)-plurisubharmonic in the sense of
Harvey-Lawson if the sum of any n-1 eigenvalues of its complex Hessian is
nonnegative. We show that the associated Monge-Ampere equation can be solved on
any compact Kahler manifold. As a consequence we prove the existence of
solutions to an equation of Fu-Wang-Wu, giving Calabi-Yau theorems for
balanced, Gauduchon and strongly Gauduchon metrics on compact Kahler manifolds.

Differential Geometry;Complex Variables