Weak lineal convexity (Q2791820)

\textit{C. Kiselman} in [Math. Ann. 311, No. 1, 1--10 (1998; Zbl 0911.32031)] claimed that the so-called Behnke-Peschl differential condition implies that a domain in \(\mathbb C^n\) with \(\mathcal C^2\)-boundary is weakly lineally convex. However, \textit{Y. Zelinskiĭ} in [Ukr. Math. J. 54, No. 2, 345--349 (2002; Zbl 1010.52001), translation from Ukr. Mat. Zh. 54, No. 2, 280--284 (2002)] presented a counterexample in the unbounded case.NEWLINENEWLINEIn the paper under review the author constructs an explicit example of a \(\mathcal C^{\infty}\)-smooth unbounded Hartogs domain in \(\mathbb C^2\) which satisfies the Behnke-Peschl condition but is not weakly lineally convex.NEWLINENEWLINEFor the entire collection see [Zbl 1337.41001].