CR functions on subanalytic hypersurfaces

Debraj Chakrabarti, Rasul Shafikov

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


A general class of singular real hypersurfaces, called subanalytic, is defined. For a subanalytic hypersurface M in ℂn;, Cauchy-Riemann (or simply CR) functions on M are defined, and certain properties of CR functions discussed. In particular, sufficient geometric conditions are given for a point p on a subanalytic hypersurface M to admit a germ at p of a smooth CR function f that cannot be holomorphically extended to either side of M. As a consequence it is shown that a well-known condition of the absence of complex hypersurfaces contained in a smooth real hypersurface M, which guarantees one-sided holomorphic extension of CR functions on M, is neither a necessary nor a sufficient condition for one-sided holomorphic extension in the singular case.

Original languageEnglish
Pages (from-to)459-494
Number of pages36
JournalIndiana University Mathematics Journal
Issue number2
StatePublished - 2010


  • CR functions
  • Holomorphic extension
  • Singular hypersurfaces


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