Kolodziej's subsolution theorem for unbounded pseudoconvex domains

• Authors: Per Åhag , Rafał Czyż

Abstracts

EN

In this paper we generalize Kolodziej's subsolution theorem to bounded and unbounded pseudoconvex domains, and in that way we are able to solve complex Monge-Ampère equations on general pseudoconvex domains. We then give a negative answer to a question of Cegrell and Kolodziej by constructing a compactly supported Radon measure $\mu$ that vanishes on all pluripolar sets in $C^n$ such that $\lambda(C^n)=(2\pi)^n$, and for which there is no function $u$ in $\mathcal L_+$ such that $(dd^cu)^n=\mu$. We end this paper by solving a Monge_Amp±re type equation. Furthermore, we prove uniqueness and stability of the solution.

• Publisher: Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
• Journal: Universitatis Iagellonicae Acta Mathematica
• Year: 2012
• Volume: 50
• Pages: 7-23

Dates

published

2012

Contributors

author

Per Åhag

author

Rafał Czyż

Identifiers

Biblioteka Nauki

1368153