This article is cited in 4 papers

On fibering into analytic curves of the common boundary of two domains of holomorphy

N. V. Shcherbina


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 $C^1$ smooth hypersurface in $\mathbf C^2$ 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.

UDC: 517.5

MSC: Primary 32D05; Secondary 32C25

Received: 29.03.1982

 English version: Mathematics of the USSR-Izvestiya, 1983, 21:2, 399–413

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