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Examples on an extension problem of holomorphic maps and a holomorphic 1- dimensional foliation. (English) Zbl 0718.32014
Let \(\partial B(\epsilon)=\{z\in {\mathbb{C}}^ 2:\) \(1-\epsilon <\| z\| <j1\}\). The author constructs:
(1) a complex 3-dimensional manifold M and a holomorphic mapping f: \(\partial B(\epsilon)\to M\) such that for each point z with \(\| z\| =1-\epsilon\) there is no neighbourhood W of z such that f extends holomorphically to \(W\cup \partial B(\epsilon);\)
(2) a 1-dimensional holomorphic foliation on P(TM) which shows that a theorem of Nishino is not true in higher codimensions.

MSC:
32D15 Continuation of analytic objects in several complex variables
32A40 Boundary behavior of holomorphic functions of several complex variables
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