$C^\infty$ extensions of holomorphic functions from subvarieties of a convex domain
Bull. Korean Math. Soc. 2001 Vol. 38, No. 3, 487-493
Hong Rae Cho
Andong National University
Abstract : Let $\Omega$ be a bounded convex domain in $\Bbb C^n$ with smooth boundary. Let $M$ be a subvariety of $\Omega$ which intersects $\partial\Omega$ transversally. Suppose that $\Omega$ is totally convex at any point of $\partial M$ in the complex tangential directions. For $f\in{\Cal O}(M)\cap C^\infty(\overline M)$, there exists $F\in \Cal O(\Omega)\cap C^\infty(\overline\Omega)$ such that $F(z)=f(z)$ for $z\in M$.
Keywords : $C^\infty$ extensions of holomorphic functions from subvarieties, convex domains, totally convex
MSC numbers : 32A26, 32A10, 32A40
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