We give a positive answer to Gromov's question [Oka's principle for holomorphic sections of elliptic bundles, J. Amer. Math. Soc. 2 (1989) 851–897, 3.4.(D), p. 881]: If every holomorphic map from a compact convex set in a Euclidean space to a certain complex manifold Y is a uniform limit of entire maps , then Y enjoys the parametric Oka property. In particular, for any reduced Stein space X the inclusion of the space of holomorphic maps into the space of continuous maps is a weak homotopy equivalence.
Nous donnons une réponse positive à la question suivante posée par Gromov [Oka's principle for holomorphic sections of elliptic bundles, J. Amer. Math. Soc. 2 (1989) 851–897, 3.4.(D), p. 881] : Si une variété analytique complexe Y est telle que toute application holomorphe d'un voisinage d'un sous-ensemble compact convexe de l'espace euclidien dans Y peut être approximée par des applications entière de dans Y, alors les applications holomorphes d'un espace de Stein réduit X dans Y possèdent la propriété d'Oka paramétrique.
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@article{CRMATH_2009__347_17-18_1017_0, author = {Forstneri\v{c}, Franc}, title = {Oka manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {1017--1020}, publisher = {Elsevier}, volume = {347}, number = {17-18}, year = {2009}, doi = {10.1016/j.crma.2009.07.005}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.07.005/} }
Forstnerič, Franc. Oka manifolds. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1017-1020. doi : 10.1016/j.crma.2009.07.005. http://www.numdam.org/articles/10.1016/j.crma.2009.07.005/
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