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Nikolay Shcherbina

On defining functions for unbounded pseudoconvex domains

We show that there exist an unbounded strictly pseudoconvex domain $\Omega\subset\mathbb C^n$ and a Wemer type set $\mathcal E\subset\Omega$ such that each defining function for $\Omega$ fails to be strictly plurisubharmonic on $\mathcal E$. We also prove a Liouville theorem for
Wermer type sets.








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