Abstract:
A description is given of the set of those boundary points of a domain of holomorphy D⊂C2 which have a neighborhood in which the boundary fibers into analytic curves. For domains with C1-smooth boundary whose closure has a basis of Stein neighborhoods this set coincides with the complement of the Shilov boundary SA(¯¯¯¯¯D).
Bibliography: 5 titles.
Citation:
N. V. Shcherbina, “The Levi form for C1-smooth hypersurfaces, and the complex structure on the boundary of domains of holomorphy”, Math. USSR-Izv., 19:1 (1982), 171–188
\Bibitem{Shc81}
\by N.~V.~Shcherbina
\paper The Levi form for $C^1$-smooth hypersurfaces, and the complex structure on the boundary of domains of holomorphy
\jour Math. USSR-Izv.
\yr 1982
\vol 19
\issue 1
\pages 171--188
\mathnet{http://mi.mathnet.ru/eng/im1589}
\crossref{https://doi.org/10.1070/IM1982v019n01ABEH001406}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=631442}
\zmath{https://zbmath.org/?q=an:0513.32019|0487.32009}
Linking options:
https://www.mathnet.ru/eng/im1589
https://doi.org/10.1070/IM1982v019n01ABEH001406
https://www.mathnet.ru/eng/im/v45/i4/p874
This publication is cited in the following 4 articles:
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
N. G. Kruzhilin, “Foliations connected with the Monge–Ampère equation in Hartogs domains”, Math. USSR-Izv., 25:2 (1985), 419–427
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
Citation in format AMSBIB
Contact us: