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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.

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Authors and Affiliations

  1. Department of Mathematics, Middlesex College, University of Western Ontario, N6A 5B7, London, Ontario, USA

    Rasul Shafikov

  2. Department of Mathematics, Indian Institute of Science, 560 012, Bangalore, India

    Kaushal Verma

Authors
  1. Rasul Shafikov
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  2. Kaushal Verma
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Shafikov, R., Verma, K. Boundary regularity of correspondences in ℂn . Proc. Indian Acad. Sci. (Math. Sci.) 116, 59–70 (2006). https://doi.org/10.1007/BF02829739

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