Extension of holomorphic maps between real hypersurfaces of different   dimension
  It is proved that the germ of a holomorphic map from a real analytic hypersurface M in C^n into a strictly pseudoconvex compact real algebraic hypersurface M' in C^N, 1 < n < N extends holomorphically along any path on M. 
Rasul Shafikov, Kaushal Verma