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arXiv · 0802.3265

Plurisubharmonic functions with weak singularities

S. Benelkourchi·V. Guedj·A. Zeriahi
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Abstract

We study the complex Monge-Ampère operator in bounded hyperconvex domains of $\C^n$. We introduce a scale of classes of weakly singular plurisubharmonic functions : these are functions of finite weighted Monge-Ampère energy. They generalize the classes introduced by U.Cegrell, and give a stratification of the space of (almost) all unbounded plurisubharmonic functions. We give an interpretation of these classes in terms of the speed of decreasing of the Monge-Ampère capacity of sublevel sets and solve associated complex Monge-Ampère equations.

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S. Benelkourchi, V. Guedj, A. Zeriahi. 2008-02-22. Plurisubharmonic functions with weak singularities. https://arxiv.org/abs/0802.3265

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