Finite-type conditions for real hypersurfaces in ℂn

  • John P. D'Angelo
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1268)


Finite Type Real Hypersurface Pseudoconvex Domain Bergman Kernel Levi Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BJT]
    M. S. Baouendi, H. Jacobowitz and F. Treves, On the analyticity of CR mappings, Annals of Math. 122 (1985) 365–400.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [Be 1]
    S. Bell, Biholomorphic mappings and the \(\bar \partial \)-problem, Annals of Math. 14 (1981) 103–113.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [B1]
    T. Bloom, On the contact between complex manifolds and real hypersurfaces in ℂ3, Trans. A.M.S., Vol. 263, No. 2 (1981) 515–529.MathSciNetzbMATHGoogle Scholar
  4. [B2]
    _____, Remarks on type conditions for real hypersurfaces in ℂn, pp. 14–24 in Several Complex Variables, Proc. of Internat. Conf. at Cortona, Italy, 1978.Google Scholar
  5. [BG]
    T. Bloom and I. Graham, A geometric characterization of points of type m on real hypersurfaces, J. Diff. Geometry 12 (1977) 171–182.MathSciNetzbMATHGoogle Scholar
  6. [C1]
    D. Catlin, Necessary conditions for subellipticity of the \(\bar \partial \)-Neumann problem, Annals of Math. 117 (1983) 147–171.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [C2]
    _____, Boundary invariants of pseudoconvex domains, Annals of Math. 120 (1984) 529–586.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [C3]
    _____, Subelliptic estimates for the \(\bar \partial \)-Neumann problem on pseudoconvex domains, preprint.Google Scholar
  9. [D1]
    J. D'Angelo, Real hypersurfaces, orders of contact, and applications, Annals of Math. 115 (1982) 615–637.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [D2]
    _____, Subelliptic estimates and failure of semi-continuity for orders of contact, Duke Math. J. 47 (1980) 955–957.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [D3]
    _____, Intersection theory and the \(\bar \partial \)-Neumann problem, Proc. of Symposia in Pure Mathematics (1984), Vol. 41, 51–58.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [D4]
    _____, Defining equations for real analytic hypersurfaces, Trans. A.M.S. Vol. 295, No. 1, (1986) 71–84.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [D5]
    _____, Iterated commutators and derivatives of the Levi form, preprint.Google Scholar
  14. [DF]
    K. Diederich and J. Fornaess, Pseudoconvex domains with real analytic boundaries, Annals of Math. 107 (1978) 371–384.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [DFH]
    K. Diederich, J. Fornaess and G. Herbort, Boundary behavior of the Bergman metric, Proc. of Symposia in Pure Mathematics (1984), Vol. 41, 59–67.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [G]
    P. Greiner, On subelliptic estimates of the \(\bar \partial \)-Neumann problem in ℂ2, J. Diff. Geometry 9 (1974) 239–250.MathSciNetzbMATHGoogle Scholar
  17. [He]
    G. Herbort, The boundary behavior of the Bergman kernel function and metric for a class of weakly pseudoconvex domains of ℂn, Math. Z. 184 (1983) 193–202.MathSciNetCrossRefGoogle Scholar
  18. [Ho]
    L. Ho, Subellipticity of the \(\bar \partial \)-Neumann problem on non-pseudoconvex domains, thesis, Princeton University, 1983.Google Scholar
  19. [H]
    L. Hörmander, The Analysis of Linear Partial Differential Operators III, IV, Springer-Verlag, 1985.Google Scholar
  20. [K1]
    J. Kohn, Boundary behavior of \(\bar \partial \) on weakly pseudoconvex manifolds of dimension two, J. Diff. Geometry 6 (1972) 523–542.MathSciNetzbMATHGoogle Scholar
  21. [K2]
    _____, Subellipticity of the \(\bar \partial \)-Neumann problem on pseudoconvex domains: sufficient conditions, Acta Math., Vol. 142 (1979) 79–122.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [K3]
    _____, Pseudodifferential operators and hypoellipticity, Proc. of Symposia in Pure Mathematics (1973), Vol. 23, 61–69.MathSciNetCrossRefGoogle Scholar
  23. [K4]
    _____, Estimates for \(\bar \partial _b \) on pseudoconvex manifolds, Proc. of Symposia in Pure Mathematics (1985), Vol. 43, 207–217.MathSciNetCrossRefGoogle Scholar
  24. [NSW]
    A. Nagel, E. Stein and S. Wainger, Boundary behavior of functions holomorphic in domains of finite type, Proc. Nat. Acad. of Sci. 78 (1981), No. 11, 6596–6599.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [S]
    I. Shafarevich, Basic Algebraic Geometry, Springer-Verlag, Berlin and New York, 1977.zbMATHGoogle Scholar
  26. [T]
    A. Talhoui, Conditions suffisantes de sous-ellipticité pour \(\bar \partial \), C. R. Acad. Sci. Paris, t. 296 (1983), 427–429.MathSciNetGoogle Scholar
  27. [W]
    H. Whitney, Complex Analytic Varieties, Addison Wesley Publishing Co., 1972.Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • John P. D'Angelo
    • 1
  1. 1.University of IllinoisUrbana

Personalised recommendations