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Abstract: A general class of singular real hypersurfaces, called subanalytic, isdefined.For a subanalytic hypersurface M in C^n, Cauchy-Riemann or simply CRfunctions on M are defined, and certain properties of CR functions discussed.In particular, sufficient geometric conditions are given for a point p on asubanalytic hypersurface M to admit a germ at p of a smooth CR function f thatcannot be holomorphically extended to either side of M. As a consequence it isshown that a well-known condition of the absence of complex hypersurfacescontained in a smooth real hypersurface M, which guarantees one-sidedholomorphic extension of CR functions on M, is neither a necessary nor asufficient condition for one-sided holomorphic extension in the singular case.

Autor: Debraj Chakrabarti, Rasul Shafikov


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