Boundary regularity of correspondences in ℂⁿ

Abstract

LetM, M′ be smooth, real analytic hypersurfaces of finite type in ℂⁿ and f^f^ a holomorphic correspondence (not necessarily proper) that is defined on one side of M, extends continuously up to M and maps M to M′. It is shown that f^f^ must extend across M as a locally proper holomorphic correspondence. This is a version for correspondences of the Diederich-Pinchuk extension result for CR maps.