Inventiones mathematicae

, Volume 67, Issue 3, pp 363–384

Boundary regularity of proper holomorphic mappings

  • Klas Diederich
  • John Eric Fornaess
Article

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References

  1. 1.
    Bell, S.: Non-vanishing of the Bergman kernel function at boundary points of certain domains in ℂn. Math. Ann.244, 69–74 (1979)Google Scholar
  2. 2.
    Bell, S., Ligocka, E.: A simplification and extension of Fefferman's theorem on biholomorphic mappings. Invent. Math.57, 283–289 (1980)Google Scholar
  3. 3.
    Bell, S., Boas, H.: Regularity of the Bergman projection in weakly pseudoconvex domains. Math. Ann.257, 23–40 (1981)Google Scholar
  4. 4.
    Bell, S.: Biholomorphic mappings and the\(\bar \partial \)-problem. Annals Math.114, 103–113 (1981)Google Scholar
  5. 5.
    Bell, S.: Proper holomorphic mappings and the Bergman projection. Duke Math. J.48, 167–175 (1981)Google Scholar
  6. 6.
    Bell, S.: The Bergman kernel function and proper holomorphic mappings. Preprint 1981Google Scholar
  7. 7.
    Bell, S., Catlin, D.: Proper holomorphic mappings extend smoothly to the boundary. Bulletin of AMS6 (1982) (To appear)Google Scholar
  8. 8.
    Cartan, H.: Sur les transformations analytiques des domaines cerclés et semi-cerclés bornés. Math. Ann.106 (1932)Google Scholar
  9. 9.
    Diederich, K., Fornaess, J.E.: Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions. Invent. Math.39, 129–141 (1977)Google Scholar
  10. 10.
    Diederich, K., Fornaess, J.E.: Pseudoconvex domains with real-analytic boundary. Annals Math.107, 371–384 (1978)Google Scholar
  11. 11.
    Diederich, K., Fornaess, J.E.: A remark on a paper of Bell. Manuscripta math.34, 31–44 (1981)Google Scholar
  12. 12.
    Diederich, K., Fornaess, J.E.: Proper holomorphic images of strictly pseudoconvex domains. Math. Ann.259, 279–286 (1982)Google Scholar
  13. 13.
    Diederich, K., Fornaess, J.E.: Smooth extendability of proper holomorphic mappings. Bulletin of AMS6 (1982) (To appear)Google Scholar
  14. 14.
    Diederich, K., Fornaess, J.E., Pflug, P.: Convexity in Complex Analysis. Forthcoming bookGoogle Scholar
  15. 15.
    Fefferman, Ch.: The Bergman kernel and biholomorphic mappings of pseudoconvex domains. Invent. Math.26, 1–65 (1974)Google Scholar
  16. 16.
    Kaup, W.: Über das Randverhalten von holomorphen Automorphismen beschränkter Gebiete. Manuscripta math.3, 257–270 (1970)Google Scholar
  17. 17.
    Kohn, J.J.: Harmonic integrals on strongly pseudoconvex manifolds, I and II, Annals Math.78, 112–148 (1963),79, 450–472 (1964)Google Scholar
  18. 18.
    Kohn, J.J.: Subellipticity of the\(\bar \partial \)-Neumann problem on pseudo-convex domains: sufficient conditions. Acta Math.142, 79–122 (1979)Google Scholar
  19. 19.
    Ligocka, E.: How to prove Fefferman's theorem without use of differential geometry. Ann. Pol. Math.Google Scholar
  20. 20.
    Nirenberg, L., Webster, S.M., Yang, P.: Local boundary regularity of holomorphic mappings. Comm. Pure and Appl. Math.33, 305–338 (1980)Google Scholar
  21. 21.
    Chee, P.S.: The Blaschke condition for bounded holomorphic functions. Trans. AMS148, 249–263 (1970)Google Scholar
  22. 22.
    Rudin, W.: Function theory on the ball. Grundlehren der Mathematischen Wissenschaften, Vol. 241. Berlin-Heidelberg-New York: Springer 1980Google Scholar
  23. 23.
    Webster, S.: On the proof of boundary smoothness of biholomorphic mappings. Preprint 1978Google Scholar
  24. 24.
    Webster, S.: Biholomorphic mappings and the Bergman kernel off the diagonal. Invent. Math.51, 155–169 (1979)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Klas Diederich
    • 1
  • John Eric Fornaess
    • 2
  1. 1.Universität-GHS Wuppertal, MathematikWuppertal 1Federal Republic of Germany
  2. 2.Matematisk InstituttUniversitetet i OsloOslo 3Norway

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