Wermer type sets and extension of CR functions

Abstract

For each $n\ge 2$ 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 $\Omega$ in ${\mathbb{C}}^n$ and a smooth $CR$ function $f$ on $\partial \Omega$ which has a single-valued holomorphic extension exactly to the set $\bar{\Omega }\setminus \mathcal{E}$.}

arXiv comment27 pages