Geodesic
On the analytic continuation of holomorphic mappings
Sbornik. Mathematics, Tome 27 (1975) no. 3, pp. 375-392 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $D_1$ and $D_2$ be strictly pseudoconvex domains in $\mathbf C^n$ with real analytic boundaries $\partial D_1$ and $\partial D_2$, and let $\Omega$ be a neighborhood of the point $\zeta\in\partial D_1$ with $\Omega\cap\partial D_1$ connected. Assume that the mapping $f\colon\Omega\cap\overline D_1\to\mathbf C^n$ is holomorphic in $\Omega\cap D_1$, $C_1$ in $\Omega\cap\overline D_1$, and that $f(\Omega\cap\partial D_1)\subset\partial D_2$. The author proves that $f$ can be holomorphically continued to $\Omega\cap\partial D_1$. If the domain $D_2$ is a sphere $\{|z|<1\}$ and $\partial D_1$ is simply connected, then $f$ extends to a biholomorphic mapping from $D_1$ onto $D_2$. Bibliography: 12 titles. 
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     author = {S. I. Pinchuk},
     title = {On~the analytic continuation of holomorphic mappings},
     journal = {Sbornik. Mathematics},
     pages = {375--392},
     year = {1975},
     volume = {27},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1975_27_3_a4/}
}
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S. I. Pinchuk. On the analytic continuation of holomorphic mappings. Sbornik. Mathematics, Tome 27 (1975) no. 3, pp. 375-392. http://geodesic.mathdoc.fr/item/SM_1975_27_3_a4/

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