Wermer type sets and extension of CR functions

For each $n\geq2$ we construct an unbounded closed pseudoconcave complete pluripolar set $\mathcal E$ in $\mathbb C^n$ which contains no analytic variety of positive dimension (we call it a \textit{Wermer type set}). We also construct an unbounded strictly pseudoconvex domain $Ω$ in $\mathbb C^n$ and a smooth $CR$ function $f$ on $\partialΩ$ which has a single-valued holomorphic extension exactly to the set $\barΩ\setminus\mathcal E$.}

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