Abstract
Let D, D' be arbitrary domains in C-n and C-N respectively, 1 < n <= N, both possibly unbounded and let M subset of partial derivative D, M' subset of partial derivative D' be open pieces of the boundaries. Suppose that partial derivative D is smooth real-analytic and minimal in an open neighborhood of <(M)over bar> and partial derivative D' is smooth real-algebraic and minimal in an open neighborhood of M'. Let f : D -> D' be a holomorphic mapping. Assume that the cluster set cl(f)(M) does not intersect D'. It is proved that if the cluster set cl(f) (p) of a point p is an element of M contains some point q is an element of M' and the graph of f extends as an analytic set to a neighborhood of (p, q) is an element of C-n x C-N, then f extends as a holomorphic map near p. (C) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.