| Let Gamma be a connected, smooth real-analytic, essentially finite hypersurface in Cn and let Gamma' be a compact, strictly pseudoconvex, real-algebraic hypersurface. It is proved that if f is a germ of a holomorphic mapping from Gamma to Gamma', then f extends analytically along any path on Gamma with the extension mapping Gamma to Gamma'.;It is also shown that a proper holomorphic map f from a compact domain D in Cn with a smooth real-analytic boundary to a compact domain D' with a smooth real-algebraic boundary extends holomorphically to a neighborhood of D .;The main technique used in the proof of these results is the theory of Segre Varieties and the Reflection principle. |
