Relative non-pluripolar product of currents on compact Hermitian manifolds

TL;DR

This paper establishes the well-definedness and monotonicity of the relative non-pluripolar product of currents on certain compact Hermitian manifolds, including Kähler manifolds, advancing the understanding of complex geometric measures.

Contribution

It proves the relative non-pluripolar product is always well-defined and monotonic in mass on a broad class of compact Hermitian manifolds, including Kähler manifolds.

Findings

Relative non-pluripolar product is well-defined on these manifolds.

Monotonicity of the product in terms of masses is established.

Results extend known properties from Kähler to Hermitian settings.

Abstract

On a class of compact Hermitian manifolds including compact K\"{a}hler manifolds, we prove that the the relative non-pluripolar product is always well-defined. We also prove the monotonicity of the relative non-pluripolar product in terms of masses on such manifolds.