Suppose that is a complex manifold such that any holomorphic map from a compact convex set in a Euclidean space to is a uniform limit of entire maps . We prove that a holomorphic map from a closed complex subvariety in a Stein manifold admits a holomorphic extension provided that it admits a continuous extension. We then establish the equivalence of four Oka-type properties of a complex manifold.
Soit une variété analytique complexe telle que toute application holomorphe d’une partie convexe compacte de l’espace euclidien à valeurs dans est limite uniforme d’applications entières à valeurs dans . On prouve que toute application holomorphe d’un sous ensemble analytique complexe fermé d’une variété de Stein à valeurs dans possède un prolongement holomorphe à à condition qu’elle admette un prolongement continu. On établit ensuite l’équivalence entre quatre propriétés de type Oka pour une variété analytique complexe.
Classification: 32E10, 32E30, 32H02
Keywords: Stein manifold, holomorphic mappings, Oka property
@article{AIF_2005__55_3_733_0, author = {Forstneric, Franc}, title = {Extending holomorphic mappings from subvarieties in {Stein} manifolds}, journal = {Annales de l'Institut Fourier}, pages = {733--751}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {3}, year = {2005}, doi = {10.5802/aif.2112}, mrnumber = {2149401}, zbl = {1076.32003}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2112/} }
TY - JOUR TI - Extending holomorphic mappings from subvarieties in Stein manifolds JO - Annales de l'Institut Fourier PY - 2005 DA - 2005/// SP - 733 EP - 751 VL - 55 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2112/ UR - https://www.ams.org/mathscinet-getitem?mr=2149401 UR - https://zbmath.org/?q=an%3A1076.32003 UR - https://doi.org/10.5802/aif.2112 DO - 10.5802/aif.2112 LA - en ID - AIF_2005__55_3_733_0 ER -
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. https://aif.centre-mersenne.org/articles/10.5802/aif.2112/
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