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Degenerate complex Monge-Amp\`ere equations with non-K\"ahler forms in bounded domains
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abstract
In this paper, we study weak solutions to complex Monge-Amp\`ere equations of the form $(\omega + dd^c \varphi)^n= F(\varphi,.)d\mu$ on a bounded strictly pseudoconvex domain in $\mathbb{C}^n$, where $\omega$ is a smooth $(1,1)$-form, $0\leq F$ is a continuous non-decreasing function, and $\mu$ is a positive non-pluripolar measure. Our results extend previous works of Ko{\l}odziej and Nguyen \cite{KN15,KN23a,KN23b} who study bounded solutions, as well as Cegrell \cite{Ceg98,Ceg04,Ceg08}, Czy\.z \cite{Cz09}, Benelkourchi \cite{Ben09,Ben15} and others who treat the case when $\omega=0$ and/or $F=1$.
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Weak convergence of complex Monge-Amp\`ere operators on compact Hermitian manifolds
A weak convergence criterion for non-pluripolar Monge-Ampere measures is proved under only a bounded subsolution, yielding solvability for L1 densities and an L-infinity estimate.
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