CR functions on Subanalytic Hypersurfaces

Details CR functions on Subanalytic Hypersurfaces CR functions on Subanalytic Hypersurfaces

2009-05-10

arxiv.org/abs/0905.1502v3

Mathematics

Complex Variables

Minor typos fixed. Final version. To appear in the Indiana University Mathematics Journal

Scientific paper

A general class of singular real hypersurfaces, called subanalytic, is defined. For a subanalytic hypersurface M in C^n, 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.

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