Plurisubharmonic functions with weak singularities

By S. Benelkourchi, Vincent Guedj, Ahmed Zeriahi. 2008

46 citations recorded by the source corpus.

We study the complex Monge-Amp\`ere 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-Amp\`ere 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-Amp\`ere capacity of sublevel sets and solve associated complex Monge-Amp\`ere equations.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c8332a6a7c6c4da14753392d905170b3f5b6e88f