Holomorphic correspondences between $CR$ manifolds C. HillRasul Shafikov 32V2532H99holomorphic correspondencesCR manifoldsCR mapsholomorphic maps It is proved that a germ of a real analytic CR map from a smooth real-analytic minimal CR manifold $M$ to an essentially finite real-algebraic generic submanifold $M'$ of $\mathbb{P}^N$ of the same CR-dimension extends as a holomorphic correspondence along $M$. Applications are given for pseudoconcave submanifolds of $\mathbb{P}^n$. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2504 10.1512/iumj.2005.54.2504 en Indiana Univ. Math. J. 54 (2005) 417 - 442 state-of-the-art mathematics http://iumj.org/access/