An existence theorem for non-pluripolar complex Monge-Amp\`ere type equations on hyperconvex domains

TL;DR

This paper proves an existence theorem for solutions to a class of complex Monge-Ampère equations with prescribed singularities on hyperconvex domains, advancing the understanding of complex pluripotential theory.

Contribution

It introduces a general existence result for non-pluripolar complex Monge-Ampère equations with specific singularity conditions on hyperconvex domains.

Findings

Established a general existence theorem for the equations.

Extended the theory to include prescribed singularities.

Provided new tools for solving complex Monge-Ampère equations.

Abstract

In this paper, we study the non-pluripolar complex Monge-Amp\`ere measure on bounded domains in \( \mathbb{C}^n \). We establish a general existence theorem for a non-pluripolar complex Monge-Amp\`ere type equation with prescribed singularity on a bounded hyperconvex domain in \( \mathbb{C}^n \).