Boundary regularity of correspondences in ℂn

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Abstract

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