4 problems

Let $D\subset\mathbb{C}^n$ be a domain, and let $\varphi$ be a strongly upper semi-continuous function on $D$, meaning that for every $x\in D$ and every subset $S\subset D$ of meas…

Let $D$ be a bounded complete Kähler domain in $\mathbb C^n$. The Ohsawa–Takegoshi theorem concerns $L^2$ extension of holomorphic functions from suitable complex submanifolds or h…

Pluriharmonicity characterization. The following are equivalent:

Let $X$ be a compact Kähler manifold, let $H\to X$ be a holomorphic line bundle, and let $Z\subset X$ be a smooth hypersurface. Let $h$ be a singular Hermitian metric on $H$ satisf…