Relative non-pluripolar product of currents on compact Hermitian manifolds

Abstract

Let $(X,\omega )$ be a compact Hermitian manifold. Assume that the Hermitian form $\omega$ satisfies $\partial \overline{\partial }\omega =0$, $\partial \omega \wedge \overline{\partial }\omega =0$. We prove that the relative non-pluripolar product is well-defined on $X$ and satisfies the monotonicity property, generalizing Vu's results in the Kähler setting.

Revised version, prepared for submission