Jensen measures and unbounded \(B\)-regular domains in \(\mathbb C^n\) (Q933641)

The main result of the paper is the following theorem. Let \(\Omega\subset\mathbb C^n\) be an unbounded convex \(\mathcal C^1\)-smooth domain. Assume that for every \(z\in\partial\Omega\) there exists a real hyperplane \(L_z\subset T_z\partial\Omega\) such that \((z+L_z)\cap\partial\Omega=\{z\}\). Then \(\Omega\) is \(B\)-regular. In the case where \(\Omega\) is a strictly convex \(\mathcal C^2\)-smooth domain, the above theorem generalizes a result by \textit{A.~Simioniuc} and \textit{G.~Tomassini} [Manuscr. Math. 126, 73--97 (2008; Zbl 1144.32019)].