Characterizing the range of the complex Monge-Amp\`ere operator
Complex Variables
2025-03-28 v3 Analysis of PDEs
Differential Geometry
Abstract
In this note, we solve the complex Monge-Amp\`ere equation for measures with a pluripolar part in compact K\"ahler manifolds. This result generalizes the classical results obtained by Cegrell in bounded hyperconvex domains. We also discuss the properties of the complex Monge-Amp\`ere operator in some special cases.
Cite
@article{arxiv.2412.03445,
title = {Characterizing the range of the complex Monge-Amp\`ere operator},
author = {Songchen Liu},
journal= {arXiv preprint arXiv:2412.03445},
year = {2025}
}
Comments
11 pages, no figures. v1. comments are welcome. v3 The main result remains unchanged, and the length of the paper has been reduced