Un phénomène de Hartogsdans les variétés projectives

In this article, we study univalent open subsets , , assuming to be pseudoconcave in Andreotti's sense. We prove an Hartogs's Kugelsatz theorem for such open sets: Let U an open subset in V such that is a pseudoconcave domain in the sense of Andreotti. Then U contains a maximal compact hypersurface H. Moreover, any meromorphic section s, of a vector bundle F over V, defined on (a neighborhood of) extends on , and, if s is holomorphic then s extends meromorphically to U, with a polar set in H.

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Received November 30, 1997; in final form July 23, 1998