COMPLETE SYSTEM OF FINITE ORDER FOR CR MAPPINGS BETWEEN REAL ANALYTIC HYPERSURFACES OF DEGENERATE LEVI FORM

  • Kim, Sung-Yeon (Department of Mathematics, Pohang University of Science and Technology)
  • Published : 2001.01.01

Abstract

We prove that the germ of a CR mapping f between real analytic real hypersurfaces has a holomorphic extension and satisfies a complete system of finite order if the source is of finite type in the sense of Bloom-Graham and the target is k-nondegenerate under certain generic assumptions on f.

Keywords

References

  1. Acta Math. v.177 Algebracity of holomorphic mappings between real algebraic sets in Cⁿ M.S.Baouendi;P.Ebenfelt;L.P.Rothschild
  2. Ann.of Math. v.122 On the analyticity of CR mappings M.S.Baouendi;H.Jacobowitz;F.Treves
  3. Invent.Math. v.93 Germs of CR maps between real analytic hypersurfaces M.S.Baouendi;L.P.Rothschild
  4. Duke Math.J. v.51 About the holomorphic extension of CR functions on real hypersurfaces in complex space M.S.Baouendi;F.Treves
  5. Acta Math. v.133 Real hypersurfaces in complex manifolds S.S.Chern;J.K.Moser
  6. Duke Math.J. v.47 A reflection principle for degenerate real hypersurfaces K.Diederich;S.Webster
  7. Invent.Math. v.73 Analyticity of CR equivalences between some real hypersurfaces in Cⁿ with degenerate Levi forms C.K.Han
  8. Math.Ann. v.309 Complete differential system for the mappings of CR manifolds of nondegenerate Levi forms
  9. J.Korean Math.Soc. Equivalence problem and complete system of finite order C.K.Han
  10. Osaka J.of Math. v.35 On the complete system of finite order for CR mappings and its application A.Hayashimoto
  11. A reflection principle for real-analytic submanifolds of complex spaces B.Lamel
  12. Acad.Naz.Lincei v.35 On the boundary behavior of holomorphic mappings H.Lewy
  13. Applications of Lie groups to differential equations(Second edition) P.J.Olver
  14. Mat.Sbornik v.98 On the analytic continuation of holomorphic mappings S.I.Pincuk
  15. Math.USSR Sbornik v.27 On the analytic continuation of holomorphic mappings S.I.Pincuk
  16. Invent.Math. v.43 On the mapping problem for algebraic real hypersurfaces S.Webster
  17. Proc.Amer.Math.Soc. v.71 On the reflection principle in several complex variables
  18. Math.Research Letters v.4 Germs of local automorphism of real analytic CR structures and analytic dependence on k-jets D.Zaitsev