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Izv. RAN. Ser. Mat., 2004, Volume 68, Issue 3, Pages 195–218 (Mi izv491)  

This article is cited in 1 scientific paper (total in 1 paper)

Semilocal Levi-flat extensions

N. V. Shcherbina, G. Tomassini


Abstract: 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.

DOI: https://doi.org/10.4213/im491

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English version:
Izvestiya: Mathematics, 2004, 68:3, 619–641

Bibliographic databases:

UDC: 517.553
MSC: Primary 32D10, 30H05; Secondary 32T99
Received: 09.12.2003

Citation: N. V. Shcherbina, G. Tomassini, “Semilocal Levi-flat extensions”, Izv. RAN. Ser. Mat., 68:3 (2004), 195–218; Izv. Math., 68:3 (2004), 619–641

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Tomassini G., “Recent results on the extension problem of analytic objects”, Milan J. Math., 75:1 (2007), 399–412  crossref  mathscinet  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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