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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
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