Comparison principles for Monge-Amp\`ere measures on pluripolar sets

Thai Duong Do; Hoang Hiep Pham

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arXiv · 2604.19347

Comparison principles for Monge-Amp\`ere measures on pluripolar sets

Thai Duong Do·Hoang Hiep Pham

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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.

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Thai Duong Do, Hoang Hiep Pham. 2026-04-21. Comparison principles for Monge-Amp\`ere measures on pluripolar sets. https://arxiv.org/abs/2604.19347

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