Semilocal Levi-flat extensions
Izvestiya. Mathematics , Tome 68 (2004) no. 3, pp. 619-641
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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 $\mathscr E(U)$ with respect to the algebra $\mathscr A(G\times\mathbb R)$ and study its properties. It is proved that every continuous function on $U$ can be extended to a continuous function on $\mathscr E(U)$ whose graph is locally foliated by holomorphic curves.
@article{IM2_2004_68_3_a9,
author = {N. V. Shcherbina and G. Tomassini},
title = {Semilocal {Levi-flat} extensions},
journal = {Izvestiya. Mathematics },
pages = {619--641},
publisher = {mathdoc},
volume = {68},
number = {3},
year = {2004},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2004_68_3_a9/}
}
N. V. Shcherbina; G. Tomassini. Semilocal Levi-flat extensions. Izvestiya. Mathematics , Tome 68 (2004) no. 3, pp. 619-641. http://geodesic.mathdoc.fr/item/IM2_2004_68_3_a9/