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The ends of varieties. (English) Zbl 0678.32005
The end of a variety is defined to be a set of the form \(\bar V/V\) where V is an analytic variety in an open subset of \({\mathbb{C}}^ N\). In this paper the theory of boundary behaviour of holomorphic functions of one or several variables is studied in considerable detail.
Using some elementary ideas from harmonic analysis the authors construct some discs with large ends. A result about contact manifolds is obtained and it is used in the following section to give further examples of discs with large ends. Lastly the general geometric idea of the previous section is used to show the existence of discs with arbitrarily rapidly growing area.
Reviewer: S.S.Singh

MSC:
32A40 Boundary behavior of holomorphic functions of several complex variables
32A10 Holomorphic functions of several complex variables
30E25 Boundary value problems in the complex plane
32T99 Pseudoconvex domains
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