Abstract:
An analogue of the Frobenius theorem is proved for the case of a continuous planar field. This leads to a proof that it is possible to fiber into analytic curves a C1 smooth hypersurface in C2 on both sides of which lie domains of holomorphy. An example constructed of two domains of holomorphy with common boundary which does not contain analytic subsets.
Bibliography: 5 titles.
Citation:
N. V. Shcherbina, “On fibering into analytic curves of the common boundary of two domains of holomorphy”, Math. USSR-Izv., 21:2 (1983), 399–413
\Bibitem{Shc82}
\by N.~V.~Shcherbina
\paper On fibering into analytic curves of the common boundary of two domains of holomorphy
\jour Math. USSR-Izv.
\yr 1983
\vol 21
\issue 2
\pages 399--413
\mathnet{http://mi.mathnet.ru/eng/im1663}
\crossref{https://doi.org/10.1070/IM1983v021n02ABEH001797}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=675533}
\zmath{https://zbmath.org/?q=an:0518.32008}
Linking options:
https://www.mathnet.ru/eng/im1663
https://doi.org/10.1070/IM1983v021n02ABEH001797
https://www.mathnet.ru/eng/im/v46/i5/p1106
This publication is cited in the following 4 articles:
Tobias Harz, Nikolay Shcherbina, Giuseppe Tomassini, “On defining functions and cores for unbounded domains I”, Math. Z., 286:3-4 (2017), 987
Bernard Aupetit, Complex Potential Theory, 1994, 1
E. M. Chirka, “Introduction to the geometry of CR-manifolds”, Russian Math. Surveys, 46:1 (1991), 95–197
R. A. Airapetyan, “Extension of CR-functions from piecewise smooth CR-manifolds”, Math. USSR-Sb., 62:1 (1989), 111–120
Citation in format AMSBIB
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