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2022-12-19T04:15:23Z
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Analytic Discs Attached to Half Spaces of $\Bbb C^n$ and Extension of Holomorphic Functions
Baracco, Luca
138804
Zampieri, Giuseppe
138805
415
analytic discs
holomorphic functions
application/pdf
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.
departmental bulletin paper
Graduate School of Mathematical Sciences, The University of Tokyo
2001
application/pdf
Journal of mathematical sciences, the University of Tokyo
2
8
317
327
AA11021653
13405705
https://repository.dl.itc.u-tokyo.ac.jp/record/40210/files/jms080207.pdf
eng