Skip to main content
Log in

Germs of CR maps between real analytic hypersurfaces

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. D'Angelo, J.: The notion of formal essential finiteness for smooth real hypersurfaces. Indiana J. Math.36, 897–903 (1987)

    Google Scholar 

  2. Baouendi, M.S., Bell, S., Rothschild, L.P.: CR mappings of finite multiplicity and extension of proper holomorphic mappings. Bull. Am. Math. Soc.16, 265–270 (1987)

    Google Scholar 

  3. Baouendi, M.S., Bell, S., Rothschild, L.P.: Mappings of three-dimensional CR manifolds and their holomorphic extension. Duke Math. J. (to appear)

  4. Baouendi, M.S., Jacobowitz, H., Treves, F.: On the analyticity of CR mappings. Ann. Math.122, 365–400 (1985)

    Google Scholar 

  5. Baouendi, M.S., Rothschild, L.P.: CR mappings and their holomorphic extension. Proceedings “Journées Equations aux Derivées Partielles” Saint-Jean-de-Monts, June 1–5, 1987, Soc. Math. France

  6. Baouendi, M.S., Treves, F.: About the holomorphic extension of CR functions on real hypersurfaces in complex space. Duke Math. J.51, 77–107 (1984)

    Google Scholar 

  7. Bedford, E., Bell, S.: Extension of proper holomorphic mappings past the boundary. Manuscr. Math.50, 1–10 (1985)

    Google Scholar 

  8. Bell, S.: Analytic hypoellipticity of the\(\bar \partial \) problem and extendability of holomorphic mappings. Acta Math.147, 109–116 (1981)

    Google Scholar 

  9. Bell, S., Catlin, D.: Boundary regularity of proper holomorphic mappings. Duke Math. J.49, 385–396 (1982)

    Google Scholar 

  10. Bloom, T., Graham, I.: On “type” conditions for generic submanifolds ofC″. Invent. Math.40, 217–243 (1977)

    Google Scholar 

  11. Derridj, M.: Le principe de réflexion en des points de faible pseudoconvexité pour des applications holomorphes propres. Invent. Math.79, 197–215 (1985)

    Google Scholar 

  12. Diederich, K., Fornaess, J.E.: Boundary regularity of proper holomorphic mappings. Invent. Math.67, 363–384 (1982)

    Google Scholar 

  13. Diederich, K., Webster, S.M.: A reflection principle for degenerate real hypersurfaces. Duke Math. J.47, 835–843 (1980)

    Google Scholar 

  14. Eisenbud, D., Levine, H.: An algebraic formula for the degree of aC map germ. Ann. Math.106, 19–44 (1977)

    Google Scholar 

  15. Fornaess, J.E.: Biholomorphic mappings between weakly pseudoconvex domains. Pac. J. Math.74, 63–65 (1978)

    Google Scholar 

  16. Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: Wiley-Interscience 1978

    Google Scholar 

  17. Han, C.K.: Analyticity of C.R. equivalence between some real hypersurfaces inC n, with degenerate Levi form. Invent. Math.73, 51–69 (1983)

    Google Scholar 

  18. Kohn, J.J.: Boundary behaviour of\(\bar \partial \) on weakly pseudoconvex manifolds of dimension two. J. Differ. Geom.6, 523–542 (1972)

    Google Scholar 

  19. Lewy, H.: On the boundary behavior of holomorphic mappings. Acad. Naz. Lincei35, 1–8 (1977)

    Google Scholar 

  20. Nagata, M.: Local rings. New York: Wiley-Interscience 1962

    Google Scholar 

  21. Pinčuk, S.I.: On proper holomorphic mappings of strictly pseudoconvex domains. Siberian Math. J.15, 909–917 (1974)

    Google Scholar 

  22. Zariski, O., Samuel, P.: Commutative algebra, Vol. 1–2. New York: Van Nostrand 1958–1960

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported by NSF Grant DMS 8603176

Supported by NSF Grant DMS 8601260

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baouendi, M.S., Rothschild, L.P. Germs of CR maps between real analytic hypersurfaces. Invent Math 93, 481–500 (1988). https://doi.org/10.1007/BF01410197

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01410197

Keywords

Navigation