Mathematische Zeitschrift

, Volume 213, Issue 1, pp 49–64 | Cite as

A reflection principle on strongly pseudoconvex domains with generic corners

  • Franc Forstneric


Real Hypersurface Pseudoconvex Domain Bergman Kernel Plurisubharmonic Function Boundary Regularity 
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  1. 1.
    Baouendi, M.S., Jacobowitz, H., Treves, F.: On the analyticity of C-R mappings. Ann. Math.122, 365–400 (1985)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Baouendi, M.S., Rothschild, L.: Germs of C-R maps between analytic real hypersurfaces. Invent. Math.93, 481–500 (1988)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Baouendi, M.S., Rothschild, L.: Geometric properties of mappings between hypersurfaces in complex space. J. Differ. Geom.31, 473–499 (1990)MATHMathSciNetGoogle Scholar
  4. 4.
    Bell, S., Catlin, D.: Boundary regularity of proper holomorphic mappings. Duke Math. J.49, 385–396 (1982)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bell, S., Catlin, D.: Regularity of C-R mappings. Math. Z.199, 357–368 (1988)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Bishop, E.: Differentiable manifolds in complex Euclidean spaces. Duke Math. J.32, 1–21 (1965)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Chirka, E.M.: Regularity of boundaries of analytic sets (in Russian). Mat. Sb., New Ser.117 (159), 291–336 (1982)MathSciNetGoogle Scholar
  8. 8.
    Coupét, B.: Construction de disques analytiques et applications. C.R. Acad. Sci. Paris, Ser. I Math.304, 427–430 (1987)MATHMathSciNetGoogle Scholar
  9. 9.
    Coupét, B.: Regularité de fonctions holomorphes sur des wedges. Can. J. Math.40, 532–545 (1988)MATHGoogle Scholar
  10. 10.
    Diederich, K., Fornæss, J.E.: Boundary regularity of proper holomorphic mappings. Invent. Math.67, 363–384 (1982)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Diederich, K., Fornæss, J.E.: Proper holomorphic mappings between real-analytic pseudoconvex domains inC n. Math. Ann.282, 681–700 (1988)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Duchamp, T., Stout, E.L.: Maximum modulus sets. Ann. Inst. Fourier31, 37–69 (1981)MATHMathSciNetGoogle Scholar
  13. 13.
    Fefferman, C.: The Bergman kernel and biholomorphic mappings of pseudoconvex domains. Invent. Math.26, 1–65 (1974)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Forstneric, F.: Mappings of strongly pseudoconvex Cauchy-Riemann manifolds In: Bedford, E. et al. (eds.) Several complex variables and complex geometry. (Proc. Symp. Pure Math., vol. 52, part 1, 59–92) Providence, RI: Am. Math. Soc. 1991Google Scholar
  15. 15.
    Forsteric, F.: An elementary proof of Fefferman's theorem. Expo. Math.10, 135–150 (1992)Google Scholar
  16. 16.
    Forstneric, F.: Mappings of quadric Cauchy-Riemann manifolds. Math. Ann.292, 163–180 (1992)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Forstneric, F.: Proper holomorphic mappings: A survey (Math. Notes, Princeton, vol. 38) Princeton: Princeton University Press 1993Google Scholar
  18. 18.
    Hill, D.C., Taiani, G.: Families of analytic discs inC n with boundaries in a prescribed C-R manifold. Ann. Sc. Norm. Super. Pisa, Cl. Sci.5, 327–380 (1978)MATHMathSciNetGoogle Scholar
  19. 19.
    Khurumov, N.: Boundary regularity of proper holomorphic mappings of strongly pseudocovex domains (in Russian). Math. Zam.48, 149–150 (1990)MATHMathSciNetGoogle Scholar
  20. 20.
    Lempert, L.: A precise result on the boundary regularity of biholomorphic mappings. Math. Z.193, 559–579 (1986)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Michel, J., Perotti, A.:c for the\(\bar \partial \)-equation on strongly pseudoconvex domains with piecewise smooth boundareis. Math. Z.203, 415–427 (1990)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Nirenberg, L., Webster, S., Yang, P.: Local boundary regularity of holomorphic mappings. Commun. Pure Appl. Math.33, 305–338 (1980)MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Pinchuk, S.I.: Holomorphic inequivalence of some classes of domains inC n (in Russian). Mat. Sb.111 (153), 61–86 (1980); English translation in Math. USSR Sb.39, no. 1 (1981)MathSciNetGoogle Scholar
  24. 24.
    Pinchuk, S.I., Chirka, E.M.: On the reflection principle for analytic sets (in Russian). Izv. Akad. Nauk SSSR52, 205–216 (1988); English translation in Math. USSR Izv.32, no. 1 (1989)Google Scholar
  25. 25.
    Pinchuk, S.J., Khasanov, S.V.: Asymptotically holomorphic functions (in Russian). Mat. Sb.134 (176), 546–555 (1987); English translation in Math. USSR Sb.62, 541–550 (1989)Google Scholar
  26. 26.
    Pinchuk, S.I., Tsyganov, S.I.: Smoothness of C-R mappings of strongly pseudoconvex hypersurfaces (in Russian). Dokl. Akad. Nauk SSSR53, 1120–1129 (1989)Google Scholar
  27. 27.
    Range, R.M.: On the topological extension to the boundary of biholomorphic maps inC n. Trans. Am. Math. Soc.216, 203–216 (1976)MATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Range, R.M., Siu, Y.T.: Uniform estimates for the\(\bar \partial \)-equation on domains with piecewise smooth strongly pseudoconvex boundaries. Math. Ann.206, 325–354 (1973)MATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Sadullaev, A.: A boundary uniqueness theorem inC n (in Russian). Mat. Sb., New Ser.101 (143) no. 4, 568–583 (1976); English translatio in Math. USSR Sb.30, no. 4 (1976)MathSciNetGoogle Scholar
  30. 30.
    Tumanov, A.E.: Finite dimensionality of group of C-R automorphisms of standard C-R manifolds and proper holomorphic mappings of Siegel domains (in Russian). Izv. Akad. Nauk SSSR52, 651–659 (1988)MATHGoogle Scholar
  31. 31.
    Tumanov, A.E.: Extending C-R functions to a wedge from manifolds of finite type (in Russian). Mat. Sb.136 (178), 128–139 (1988); English translation in Math. USSR Sb.64, 129–140 (1989)Google Scholar
  32. 32.
    Tumanov, A.E., Khenkin, G.M.: Local characterization of holomorphic automorphisms of Siegel domains (in Russian). Funkts. Anal.17, 49–61 (1983)MathSciNetGoogle Scholar
  33. 33.
    Webster, S.M.: Holomorphic mappings of domains with genric corners. Proc. Am. Math. Soc.86, 236–240 (1982)MATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Webster, S.M.: Analytic discs and the regularity of C-R mappings of real submanifolds inC n. In: Siv, Y.T. (ed.) Complex anlysis of several variables (Proc. Symp. Pure Math., vol. 41, pp. 199–208) Providence, RI: Am. Math. Soc. 1984Google Scholar
  35. 35.
    Webster, S.M.: The holomorphic contact geometry of a real hypersurface. (Preprint 1991)Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Franc Forstneric
    • 1
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA

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