Holomorphic correspondences between CR manifolds

TL;DR

This paper proves that real-analytic CR maps between certain CR manifolds extend holomorphically as correspondences, with applications to pseudoconcave submanifolds of projective space.

Contribution

It establishes the extension of CR maps as holomorphic correspondences for minimal CR manifolds into real-algebraic submanifolds, advancing understanding of CR mappings.

Findings

CR maps extend as holomorphic correspondences

Extension applies to minimal CR manifolds and algebraic submanifolds

Applications to pseudoconcave submanifolds of projective space

Abstract

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 P^N of the same CR-dimension extends as a holomorphic correspondence along M. Applications are given for pseudoconcave submanifolds of P^N.