Abstract:
Let $G$ be a domain in $\mathbb C^n$, $n\ge2$, let $A$ be a connected complex $(n-1)$-dimensional submanifold of $G$, and let $\varphi$ be a plurisubharmonic function in $G\setminus A$. We obtain conditions on the growth of $\varphi$ that guarantee the local boundedness of $\varphi$ at a point a $a\in A\subset G$ and the existence of a plurisubharmonic extension of $\varphi$ to $G$.
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