Abstract
Let D be a domain in C(n), n > 1, and f : D -> C(n) be a holomorphic map. Let U subset of C(n) be an open set such that M := partial derivative D boolean AND U 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 cl(f) (M) is contained in a closed, smooth real-algebraic hypersurface M' subset of U' of finite type, where U' is an open set in C(n). 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. To cite this article: B. Ayed, N. Ourimi, C. R. Acad. Sci. Paris, Ser. 1347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.