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Let D be an arbitrary domain in $\mathbb{C}^n$, n > 1, and $M{\subset}{\partial}D$ be an open piece of the boundary. Suppose that M is connected and ${\partial}D$ is smooth real-analytic of finite type (in the sense of D'Angelo) in a neighborhood of $\bar{M}$. Let f : $D{\rightarrow}\mathbb{C}^n$ be a holomorphic correspondence such that the cluster set $cl_f$(M) is contained in a smooth closed real-algebraic hypersurface M' in $\mathbb{C}^n$ of finite type. It is shown that if f extends continuously to some open peace of M, then f extends as a holomorphic correspondence across M. As an application, we prove that any proper holomorphic correspondence from a bounded domain D in $\mathbb{C}^n$ with smooth real-analytic boundary onto a bounded domain D' in $\mathbb{C}^n$ with smooth real-algebraic boundary extends as a holomorphic correspondence to a neighborhood of $\bar{D}$.
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참고문헌 (25)
참고문헌 신청
B. Ayed / 2009 / Analytic continuation of holomorphic mappings / C. R. Math. Acad. Sci. Paris 347 (17-18) : 1011 ~ 1016
B. Ayed / 2010 / A Local extension of proper holomorphic maps between some unbounded do- mains in Cn / Bull. Belg. Math. Soc. Simon Stevin 17 (3) : 513 ~ 534
E. M. Chirka / 1989 / Complex Analytic Sets / Kluwer Academic Publishers
F. Berteloot / 1997 / On the continuous extension of holomorphic correspon- dences / Ann. Scuola Norm. Sup. Pisa Cl. Sci 24 (4) : 747 ~ 766
J. Merker / 2002 / On wedge extendability of CR-meromorphic functions / Math. Z 241 (3) : 485 ~ 512
B. Ayed / 2010 / A Local extension of proper holomorphic maps between some unbounded do- mains in Cn / Bull. Belg. Math. Soc. Simon Stevin 17 (3) : 513 ~ 534
E. M. Chirka / 1989 / Complex Analytic Sets / Kluwer Academic Publishers
F. Berteloot / 1997 / On the continuous extension of holomorphic correspon- dences / Ann. Scuola Norm. Sup. Pisa Cl. Sci 24 (4) : 747 ~ 766
J. Merker / 2002 / On wedge extendability of CR-meromorphic functions / Math. Z 241 (3) : 485 ~ 512
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