Proceedings of the Indian Academy of Sciences - Mathematical Sciences

, Volume 116, Issue 1, pp 59-70

First online:

Boundary regularity of correspondences in ℂn

  • Rasul ShafikovAffiliated withDepartment of Mathematics, Middlesex College, University of Western Ontario
  • , Kaushal VermaAffiliated withDepartment of Mathematics, Indian Institute of Science

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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.


Correspondences Segre varieties