The Monge-Ampère equation for (n-1)-plurisubharmonic functions on a compact Kähler manifold

Valentino Tosatti, Ben Weinkove

Published 2013-05-31, updated 2016-11-15Version 3

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.