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Tr. Mat. Inst. Steklova, 2001, Volume 235, Pages 272–287 (Mi tm248)  

This article is cited in 4 scientific papers (total in 5 papers)

Levi and Trépreau Theorems for Continuous Graphs

E. M. Chirka

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Let $\Gamma\subset\mathbb C^{n+1}$ be a continuous graph over a convex domain $D\subset\mathbb C^n\times\mathbb R$ and $a\in\Gamma$ be a point such that none of the components of $(D\times\mathbb R)\setminus\Gamma$ is extendable holomorphically to $a$. Then, $a$ is contained in an $n$-dimensional holomorphic graph lying on and closed in $\Gamma$. In particular, if $\Gamma$ divides two domains of holomorphy, then it is foliated by a family of closed holomorphic hypersurfaces–graphs. These results extend and generalize the well-known theorems of E. Levi, J.-M. Trépreau (proved for $C^2$-smooth $\Gamma$), and N. Shcherbina (proved for $n=1$).

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English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 235, 261–276

Bibliographic databases:

UDC: 517.55
Received in December 2000

Citation: E. M. Chirka, “Levi and Trépreau Theorems for Continuous Graphs”, Analytic and geometric issues of complex analysis, Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin, Tr. Mat. Inst. Steklova, 235, Nauka, MAIK Nauka/Inteperiodika, M., 2001, 272–287; Proc. Steklov Inst. Math., 235 (2001), 261–276

Citation in format AMSBIB
\Bibitem{Chi01}
\by E.~M.~Chirka
\paper Levi and Tr\'epreau Theorems for Continuous Graphs
\inbook Analytic and geometric issues of complex analysis
\bookinfo Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin
\serial Tr. Mat. Inst. Steklova
\yr 2001
\vol 235
\pages 272--287
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm248}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1886587}
\zmath{https://zbmath.org/?q=an:1004.32003}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2001
\vol 235
\pages 261--276


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Chakrabarti D., Shafikov R., “Holomorphic extension of CR functions from quadratic cones”, Mathematische Annalen, 341:3 (2008), 543–573  crossref  mathscinet  zmath  isi  elib  scopus
    2. Larusson F., Shafikov R., “Schlicht Envelopes of Holomorphy and Foliations by Lines”, Journal of Geometric Analysis, 19:2 (2009), 373–389  crossref  mathscinet  zmath  isi  scopus
    3. Chakrabarti D., Shafikov R., “CR Functions on Subanalytic Hypersurfaces”, Indiana Univ Math J, 59:2 (2010), 459–494  crossref  mathscinet  zmath  isi  scopus
    4. Harz T., Shcherbina N., Tomassini G., “Wermer Type Sets and Extension of Cr Functions”, Indiana Univ. Math. J., 61:1 (2012), 431–459  crossref  mathscinet  zmath  isi  scopus
    5. A. I. Aptekarev, V. K. Beloshapka, V. I. Buslaev, V. V. Goryainov, V. N. Dubinin, V. A. Zorich, N. G. Kruzhilin, S. Yu. Nemirovski, S. Yu. Orevkov, P. V. Paramonov, S. I. Pinchuk, A. S. Sadullaev, A. G. Sergeev, S. P. Suetin, A. B. Sukhov, K. Yu. Fedorovskiy, A. K. Tsikh, “Evgenii Mikhailovich Chirka (on his 75th birthday)”, Russian Math. Surveys, 73:6 (2018), 1137–1144  mathnet  crossref  crossref  adsnasa  isi  elib
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