2009/05/10 by Debraj Chakrabarti, Chakrabarti, Debraj, Rasul Shafikov +1
Mathematics · #32B20 #32V10 #32V25 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #msc:32B20 #msc:32V10 #msc:32V25
paper · pdf · doi:10.48550/arxiv.0905.1502
Minor typos fixed. Final version. To appear in the Indiana University Mathematics Journal
openalex publication_date 2009/05/10 · arxiv created 2009/11/20 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.