Examples on an extension problem of holomorphic maps and a holomorphic 1- dimensional foliation. (English) Zbl 0718.32014

Kato, Masahide

Tokyo J. Math. 13, No. 1, 139-146 (1990).

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.

Reviewer: M.Jarnicki (Kraków)

MSC:

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

Keywords:

holomorphic extension; boundary behaviour; holomorphic mapping; 1- dimensional holomorphic foliation; theorem of Nishino