IUMJ

Title: Wermer type sets and extension of CR functions

Authors: Tobias Harz, Nikolay Shcherbina and Giuseppe Tomassini

Issue: Volume 61 (2012), Issue 1, 431-459

Abstract:

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 $\bar{\Omega}\setminus\mathcal{E}$.