اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدEuclidean domains in complex manifolds
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Franc Forstneric
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In this paper we find big Euclidean domains in complex manifolds. We consider open neighbourhoods of sets of the form $Kcup M$ in a complex manifold $X$, where $K$ is a compact $mathscr O(U)$-convex set in an open Stein neighbourhood $U$ of $K$, $M$ is an embedded Stein submanifold of $X$, and $Kcap M$ is compact and $mathscr O(M)$-convex. We prove a Docquier-Grauert type theorem concerning biholomorphic equivalence of neighbourhoods of such sets, and we give sufficient conditions for the existence of Stein neighbourhoods of $Kcup M$, biholomorphic to domains in $mathbb C^n$ with $n=dim X$, such that $M$ is mapped onto a closed complex submanifold of $mathbb C^n$.
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