no. 3
Extending holomorphic mappings from subvarieties in Stein manifolds
[Prolongements holomorphes dans les variétés de Stein]
Forstneric, Franc1
1 Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000 Ljubljana (Slovenia)
Annales de l'Institut Fourier, Tome 55 (2005) no. 3, pp. 733-751.

Soit Y une variété analytique complexe telle que toute application holomorphe d’une partie convexe compacte de l’espace euclidien ℂ n à valeurs dans Y est limite uniforme d’applications entières à valeurs dans Y. On prouve que toute application holomorphe d’un sous ensemble analytique complexe fermé X 0 d’une variété de Stein X à valeurs dans Y possède un prolongement holomorphe à X à condition qu’elle admette un prolongement continu. On établit ensuite l’équivalence entre quatre propriétés de type Oka pour une variété analytique complexe.

Suppose that Y is a complex manifold such that any holomorphic map from a compact convex set in a Euclidean space ℂ n to Y is a uniform limit of entire maps ℂ n →Y. We prove that a holomorphic map X 0 →Y from a closed complex subvariety X 0 in a Stein manifold X admits a holomorphic extension X→Y provided that it admits a continuous extension. We then establish the equivalence of four Oka-type properties of a complex manifold.

DOI : 10.5802/aif.2112
Classification : 32E10, 32E30, 32H02
Keywords: Stein manifold, holomorphic mappings, Oka property
Mot clés : variétés de Stein, applications holomorphes, propriété d'Oka

Forstneric, Franc 1

1 Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000 Ljubljana (Slovenia) 
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Forstneric, Franc. Extending holomorphic mappings from subvarieties in Stein manifolds. Annales de l'Institut Fourier, Tome 55 (2005) no. 3, pp. 733-751. doi : 10.5802/aif.2112. https://aif.centre-mersenne.org/articles/10.5802/aif.2112/

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