Comptes Rendus
Complex Analysis
Analytic continuation of holomorphic mappings
[Continuation analytique d'applications holomorphes]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1011-1016.

Soient D un domaine de Cn, n>1, et f:DCn une application holomorphe. Soit UCn un ouvert tel que M:=DU est une hypersurface relativement fermée dans U, connexe, lisse, analytique réelle et de type fini (au sens de D'Angelo). Supposons que l'ensemble des points limites clf(M) est contenu dans une hypersurface, fermée, lisse, algébrique réelle MU de type fini, où U est un ouvert de Cn. Nous montrons que si f se prolonge continûment sur une partie ouverte de M, alors elle se prolonge holomorphiquement au voisinage de chaque point de M. Notons qu'ici la compacité de M n'est pas exigée.

Let D be a domain in Cn, n>1, and f:DCn be a holomorphic map. Let UCn be an open set such that M:=DU is in U a relatively closed, connected, smooth real-analytic hypersurface of finite type (in the sense of D'Angelo). Suppose that the cluster set clf(M) is contained in a closed, smooth real-algebraic hypersurface MU of finite type, where U is an open set in Cn. It is shown that if f extends continuously to some open piece of M, then it extends holomorphically to a neighborhood of each point of M. Note that here the compactness of M is not required.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.07.001

Besma Ayed 1 ; Nabil Ourimi 2

1 Faculté des sciences de Monastir, route de Kairouan, Monastir, 5019, Tunisia
2 King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
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Besma Ayed; Nabil Ourimi. Analytic continuation of holomorphic mappings. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1011-1016. doi : 10.1016/j.crma.2009.07.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.07.001/

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