Mathematische Annalen

, Volume 279, Issue 2, pp 239–252 | Cite as

Localization of the Kobayashi metric and the boundary continuity of proper holomorphic mappings

  • Franc Forstneric
  • Jean-Pierre Rosay


Holomorphic Mapping Boundary Continuity Proper Holomorphic Mapping 
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  1. 1.
    Alexander, H.: Holomorphic mappings from the ball and polydisk. Math. Ann.209, 249–256 (1974)Google Scholar
  2. 2.
    Alexander, H.: Proper holomorphic mappings in ℂn. Indiana Univ. Math. J.26, 137–146 (1977)Google Scholar
  3. 3.
    Bedford, E., Fornaess, J.E.: Biholomorphic maps of weakly pseudoconvex domains. Duke Math. J.45, 711–719 (1978)Google Scholar
  4. 4.
    Barrett, D.: Regularity of the Bergman projection on domains with transverse symmetries. Math. Ann.258, 441–446 (1982)Google Scholar
  5. 5.
    Bell, S., Boas, H.: Regularity of the Bergman projection in weakly pseudoconvex domains. Math. Ann.257, 23–30 (1981)Google Scholar
  6. 6.
    Bell, S., Catlin, D.: Boundary regularity of proper holomorphic mappings. Duke Math. J.49, 385–396 (1982)Google Scholar
  7. 7.
    Bell, S., Ligocka, E.: A simplification and extension of Fefferman's theorem on biholomorphic mappings. Invent. Math.57, 283–289 (1980)Google Scholar
  8. 8.
    Carathéodory, C.: Über die Begrenzung einfachzusammenhängender Gebiete. Math. Ann.73, 323–370 (1913)Google Scholar
  9. 9.
    Čirka, E.M.: Regularity of boundaries of analytic sets. Mat. Sb. (NS)117, 291–334 (1982) [English transl. Math. USSR Sb.45, 291–336 (1983)]Google Scholar
  10. 10.
    Diederich, K., Fornaess, J.E.: Proper holomorphic maps onto pseudoconvex domains with real-analytic boundary. Ann. Math.110, 575–592 (1979)Google Scholar
  11. 11.
    Diederich, K., Fornaess, J.E.: Biholomorphic mappings between two-dimensional Hartogs domains with real-analytic boundaries. In: Recent developments in several complex variables. Princeton ××× 1981Google Scholar
  12. 12.
    Diederich, K., Fornaess, J.E.: Boundary regularity of proper holomorphic mappings. Invent. Math.67, 363–384 (1982)Google Scholar
  13. 13.
    Diederich, K., Fornaess, J.E.: Biholomorphic mappings between certain real analytic domains in ℂ2. Math. Ann.245, 255–272 (1979)Google Scholar
  14. 14.
    Fefferman, C.: The Bergman kernel and biholomorphic mappings of pseudoconvex domains. Invent. Math.26, 1–65 (1974)Google Scholar
  15. 15.
    Forstnerič, F.: On the boundary regularity of proper mappings. Ann. Sc. Norm. Sup. Pisa. cl. Sc. ser. IV,13, 109–128 (1986)Google Scholar
  16. 16.
    Forstnerič, F.: Embedding strictly pseudoconvex domains into balls. Trans. Am. Math. Soc.295, 347–368 (1986)Google Scholar
  17. 17.
    Fridman, B.: One example of the boundary behaviour of biholomorphic transformation. Proc. Am. Math. Soc.89, 226–228 (1983)Google Scholar
  18. 18.
    Globevnik, J.: Boundary interpolation by proper holomorphic maps. Math. Z.194, 365–373 (1987)Google Scholar
  19. 19.
    Globevnik, J., Stout, E.L.: Boundary regularity for holomorphic maps from the disk to the ball. Preprint. Math. Scand. To appearGoogle Scholar
  20. 20.
    Globevnik, J., Stout, E.L.: The ends of varieties. Am. J. Math.108, 1355–1410 (1986)Google Scholar
  21. 21.
    Graham, I.: Boundary behaviour of the Carathéodory and Kobayashi metrics on strongly pseudoconvex domains in ℂn with smooth boundary. Trans. Am. Math. Soc.207, 219–240 (1975)Google Scholar
  22. 22.
    Harvey, F.R., Lawson, H.B.: On boundaries of complex analytic varieties. I. Ann. Math.102, 223–290 (1975)Google Scholar
  23. 23.
    Hörmander, L.: An introduction to complex analysis in several variables. Amsterdam: North-Holland 1973Google Scholar
  24. 24.
    Kaup, W.: Über das Randverhalten von holomorphen Automorphismen beschränkter Gebiete. Manuscr. Math.3, 257–270 (1970)Google Scholar
  25. 25.
    Khenkin, G.M.: Analytic polyhedron is not biholomorphically equivalent to a strictly pseudoconvex domain. Dokl. Akad Nauk SSSR210, 858–862 (1973); English transl. in Math USSR Dokl.14, 858–862 (1973)Google Scholar
  26. 26.
    Kobayashi, S.: Intrinsic distances, measures and geometric function theory. Bull. Am. Math. Soc.82, 357–416 (1976)Google Scholar
  27. 27.
    Lempert, L.: On the boundary behaviour of holomorphic mappings. PreprintGoogle Scholar
  28. 28.
    Löw, E.: Embeddings and proper holomorphic maps of strictly pseudoconvex domains into polydiscs and balls. Math. Z.190, 401–410 (1985)Google Scholar
  29. 29.
    Margulis, G.A.: Correspondence of boundaries during biholomorphic mapping of multidimensional domains. All-Union Conference on the Theory of Complex Variable Functions (in Russian), FTINT, Kharkov 1971Google Scholar
  30. 30.
    Pinčuk, S.I.: On proper holomorphic mappings of strictly pseudoconvex domains. Sib. Math. J.15, 644–649 (1975)Google Scholar
  31. 31.
    Range, M.: On the topological extension to the boundary of biholomorphic maps in ℂn. Trans AMS216, 203–216 (1976)Google Scholar
  32. 32.
    Range, M.: The Carathéodory metric and holomorphic maps on a class of weakly pseudoconvex domains. Pac. J. Math.78, 173–189 (1978)Google Scholar
  33. 33.
    Royden, H.L.: Remarks on the Kobayashi metric. Several complex variables. II. Proc. Inv. Conf. Univ. of Maryland 1970. J. Horvath (Ed.) Lect. Notes Math.185, Berlin, Heidelberg, New York: Springer 1971Google Scholar
  34. 34.
    Rudin, W.: Function theory on the unit ball of ℂn. Berlin, Heidelberg, New York: Springer 1980Google Scholar
  35. 35.
    Rudin, W.: Peak-interpolation sets of class\(C^1 \). Pac. J. Math.75, 267–279 (1978)Google Scholar
  36. 36.
    Sadullaev, A.: A boundary uniqueness theorem in ℂn. Russian: Mat. Sb. (N.S.)101 (143), 568–583 (1976); English: Math. USSR Sb. (N.S.)30, 501–514 (1976)Google Scholar
  37. 37.
    Vormoor, N.: Topologische Fortsetzung biholomorpher Funktionen auf dem Rand bei beschränkten streng-pseudokonvexen Gebieten in ℂn. Math. Ann.204, 239–261 (1973)Google Scholar
  38. 38.
    Goluzin, G.M.: Geometric theory of function of a complex variable. Transl. of Math. Monographs vol 26, AMS (1969)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Franc Forstneric
    • 1
  • Jean-Pierre Rosay
    • 2
  1. 1.Institute of Mathematics, Physics and MechanicsUniversity E.K. of LjubljanaLjubljanaYugoslavia
  2. 2.UER de Mathématiques et CNRS UA 225Université de Provence 61000Marseille Cedex 3France

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