Shcherbina, N. V.; Tomassini, Dzh. Semilocal Levi-flat extensions. (English. Russian original) Zbl 1104.32301 Izv. Math. 68, No. 3, 619-641 (2004); translation from Izv. Ross. Akad. Nauk Ser. Mat. 68, No. 3, 195-218 (2004). Summary: Let \(G\subset\mathbb{C}\times\mathbb{R}\) be a domain such that \(G\times \mathbb{R}\subset \mathbb{C}^2\) is strictly pseudoconvex and let \(U\subset bG\) be an open subset.We define the hull \({\mathcal E}(U)\) with respect to the algebra \({\mathcal A}(G\times\mathbb{R})\) and study its properties. It is proved that every continuous function on \(U\) can be extended to a continuous function on \({\mathcal E}(U)\) whose graph is locally foliated by holomorphic curves. MSC: 32E20 Polynomial convexity, rational convexity, meromorphic convexity in several complex variables 32T15 Strongly pseudoconvex domains 32T05 Domains of holomorphy PDFBibTeX XMLCite \textit{N. V. Shcherbina} and \textit{Dzh. Tomassini}, Izv. Math. 68, No. 3, 619--641 (2004; Zbl 1104.32301); translation from Izv. Ross. Akad. Nauk Ser. Mat. 68, No. 3, 195--218 (2004) Full Text: DOI