Wermer type sets and extension of CR functions Tobias HarzN. ShcherbinaGiuseppe Tomassini 32D1032V1032T1532D2032V25envelopes of holomorphy$CR$ functionsstrictly pseudoconvex domainsanalytic structure For each $n\geq 2$ 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 \emph{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 $\bar{\Omega}\setminus\mathcal{E}$. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4507 10.1512/iumj.2012.61.4507 en Indiana Univ. Math. J. 61 (2012) 431 - 459 state-of-the-art mathematics http://iumj.org/access/