Let $M$ be a real hypersurface of $\C^n$, $M^+$ a closed half space with boundary $M$, $z_o$ a point of $M$. We prove that the existence of a disc $A$ tangent to $M$ at $z_o$, attached to $M^+$ but not to $M$ (i.e.$\partial A \subset M^+$ but $\partial A \
ot\subset M$), entails extension of holomorphic functions from the interior of ${M^+}$ to a full neighborhood of $z_o$. This result covers a result in \cite{9}, where the disc $A$ is assumed to lie on one side $M^+$ of $M$. The basic idea, which underlies to the whole paper, is due to A. Tumanov [8] and consists in attaching discs to manifolds with boundary. Further, holomorphic extendability by the aid of tangent discs attached to $M$ and of ""defect 0"" is a particular case of a general theorem of ""wedge extendibility"" of CR--functions by A. Tumanov.
雑誌名
Journal of mathematical sciences, the University of Tokyo
巻
8
号
2
ページ
317 - 327
発行年
2001
ISSN
13405705
書誌レコードID
AA11021653
フォーマット
application/pdf
日本十進分類法
415
Mathematical Reviews Number
MR1837166
Mathmatical Subject Classification
58G(MSC1991)
32F(MSC1991)
出版者
Graduate School of Mathematical Sciences, The University of Tokyo
原稿受領日
2000-07-17
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Analytic Discs Attached to Half Spaces of $\Bbb C^n$ and Extension of Holomorphic Functions
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