TY - JOUR

T1 - CR functions on subanalytic hypersurfaces

AU - Chakrabarti, Debraj

AU - Shafikov, Rasul

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - CR functions

KW - Holomorphic extension

KW - Singular hypersurfaces

UR - http://www.scopus.com/inward/record.url?scp=79954438246&partnerID=8YFLogxK

U2 - 10.1512/iumj.2010.59.4125

DO - 10.1512/iumj.2010.59.4125

M3 - Article

AN - SCOPUS:79954438246

SN - 0022-2518

VL - 59

SP - 459

EP - 494

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

IS - 2

ER -