ON BOUNDARY REGULARITY OF HOLOMORPHIC CORRESPONDENCES Ourimi, Nabil;
Let D be an arbitrary domain in , n > 1, and be an open piece of the boundary. Suppose that M is connected and is smooth real-analytic of finite type (in the sense of D'Angelo) in a neighborhood of . Let f : be a holomorphic correspondence such that the cluster set (M) is contained in a smooth closed real-algebraic hypersurface M' in of finite type. It is shown that if f extends continuously to some open peace of M, then f extends as a holomorphic correspondence across M. As an application, we prove that any proper holomorphic correspondence from a bounded domain D in with smooth real-analytic boundary onto a bounded domain D' in with smooth real-algebraic boundary extends as a holomorphic correspondence to a neighborhood of .