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Let M be a real analytic strictly pseudoconvex manifold of higher codimensionin complex space, and let M' be the cartesian product of two or more compactreal analytic strictly convex hypersurfaces. We prove that a germ of abiholomorphic map taking an open set in M to M' extends as a biholomorphic mapalong any path in M.

Extremal discs and analytic continuation of product CR maps