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arXiv · 2412.03445

Characterizing the range of the complex Monge-Amp\`ere operator

Songchen Liu
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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.

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BibTeXRIS

Songchen Liu. 2024-12-04. Characterizing the range of the complex Monge-Amp\`ere operator. https://arxiv.org/abs/2412.03445

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