Work

Comparison principles for Monge-Ampère measures on pluripolar sets

Year: 2026

Type: preprint

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--Ampère 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--Ampère equation.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2604.19347

Authors: Do, Thai Duong, Pham, Hoang Hiep

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Research Foundation, National University of Singapore

OpenAlex ID: W7155170636

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