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

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.

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.

DOI: 10.5802/aif.2112
Classification: 32E10, 32E30, 32H02
Keywords: Stein manifold, holomorphic mappings, Oka property
Mots-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) 
Forstneric, Franc. Extending holomorphic mappings from subvarieties in Stein manifolds. Annales de l'Institut Fourier, Volume 55 (2005) no. 3, pp. 733-751. doi: 10.5802/aif.2112
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