CR functions on subanalytic hypersurfaces

Abstract

Abstract. 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.