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arXiv · 2003.12501

Intersection of (1,1)-currents and the domain of definition of the Monge-Ampere operator

Dinh Tuan Huynh·Lucas Kaufmann·Duc-Viet Vu
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Abstract

We study the Monge-Amp\` ere operator within the framework of Dinh-Sibony's intersection theory defined via density currents. We show that if $u$ is a plurisubharmonic function belonging to the Blocki-Cegrell class, then the Dinh-Sibony $n$-fold self-product of $\text{dd}^c u$ exists and coincides with the classically defined Monge-Amp\`ere measure $(\text{dd}^c u)^n$.

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Dinh Tuan Huynh, Lucas Kaufmann, Duc-Viet Vu. 2020-03-27. Intersection of (1,1)-currents and the domain of definition of the Monge-Ampere operator. https://arxiv.org/abs/2003.12501

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