Comparison principles for Monge-Amp\`ere measures on pluripolar sets
Complex Variables
2026-04-22 v1
Abstract
In this paper, we introduce a notion of singularity comparison for plurisubharmonic functions based on the Bedford--Taylor capacity. We establish comparison principles for the complex Monge--Amp\`ere operator on pluripolar sets in the Cegrell classes. As applications, we obtain a characterization of this relation via auxiliary functions in the energy class and prove a corresponding uniqueness result for the Monge--Amp\`ere equation.
Keywords
Cite
@article{arxiv.2604.19347,
title = {Comparison principles for Monge-Amp\`ere measures on pluripolar sets},
author = {Thai Duong Do and Hoang Hiep Pham},
journal= {arXiv preprint arXiv:2604.19347},
year = {2026}
}