THE MONGE-AMPERE EQUATION FOR (n-1)-PLURISUBHARMONIC FUNCTIONS ON A COMPACT KAHLER MANIFOLD

A C2 function on ℂn is called (n-1)-plurisubharmonic in the sense of Harvey-Lawson if the sum of any n-1 eigenvalues of its complex Hessian is non-negative. We show that the associated Monge-Ampère equation can be solved on any compact Kähler 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 Kähler manifolds. © 2016 American Mathematical Society.