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Biholomorphic self-maps of domains

Special Year Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 1276)

Keywords

  • Automorphism Group
  • Pseudoconvex Domain
  • Bergman Kernel
  • Circular Domain
  • Tube Domain

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References

  1. R. Abraham, Bumpy metrics, Proc. Symp. Pure Math.-XIV, Amer. Math. Soc., Providence, 1970, 1–4.

    Google Scholar 

  2. E. Bedford, Invariant forms on complex manifolds with applications to holomorphic mappings, Math. Ann. 265 (1983), 377–396.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. E. Bedford and J. Dadok, Bounded domains with prescribed automorphism groups, preprint.

    Google Scholar 

  4. S. Bell, Biholomorphic mappings and the \(\bar \partial\) problem, Ann. Math. 114 (1981), 103–112.

    CrossRef  Google Scholar 

  5. S. Bell and E. Ligocka, A simplification and extension of Fefferman’s theorem on biholomorphic mappings, Invent. Math. 57 (1980), 283–289.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. L. Bers, Riemann Surfaces, Stevens, New York, 1959.

    MATH  Google Scholar 

  7. M. Berger, Pincement riemannien et pincement holomorphe, Ann. Scuola Norm. Sup. Pisa 14 (1960), 151–159.

    MathSciNet  MATH  Google Scholar 

  8. J. Bland, T. Duchamp, and M. Kalka, A characterization of ℂℙn by its automorphism group, Proceedings of the Complex Analysis Week at Penn State, Springer Verlag, to appear.

    Google Scholar 

  9. R. Braun, W. Karp, and H. Upmeier, On the automorphisms of circular and Reinhardt domains in complex Banach spaces, Manuscripta Mat. 25 (1978), 97–133.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. D. Burns and S. Shnider, Geometry of hypersurfaces and mapping theorems in ℂn, Comment. Math. Helv. 54 (1979), 199–217.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. D. Burns, S. Shnider, and R. Wells, On deformations of strictly pseudoconvex domains, Inventiones Math. 46(1978), 237–253.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. S. Chern and J. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133(1974), 219–271.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. J. D’Angelo, Hypersurfaces, orders of contact and applications, Ann. Math. 115 (1982), 615–638.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. D. Ebin, The manifold of Riemannian metrics, Proc. Symp. Pure Math. XV, Am. Math. Soc., Providence, 1970.

    Google Scholar 

  15. H. Farkas and I. Kra, Riemann Surfaces, Springer, New York, 1974.

    MATH  Google Scholar 

  16. C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26(1974), 1–65.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. G. B. Folland and J. J. Kohn, The Neumann Problem for the Cauchy-Riemann Complex, Princeton University Press, Princeton, 1972.

    MATH  Google Scholar 

  18. B. A. Fuks, Special Chapters in the Theory of Analytic Functions of Several Complex Variables, Trans. Amer. Math. Soc., Providence, 1965.

    MATH  Google Scholar 

  19. I. Graham, Boundary behavior of the Caratheodory and Kobayashi metrics on strongly pseudoconvex domains in ℂn with smooth boundary, Trans. Am. Math. Soc. 207(1975), 219–240.

    MathSciNet  MATH  Google Scholar 

  20. R. E. Greene and S. G. Krantz, Stability of the Bergman kernel and curvature properties of bounded domains, in Recent Developments in Several Complex Variables, Annals of Math. Studies 100, Princeton University Press, Princeton, 1981.

    Google Scholar 

  21. R. E. Greene and S. G. Krantz, Deformations of complex structures, estimates for the \(\bar \partial\) equation, and stability of the Bergman kernel, Adv. Math 43(1982), 1–86.

    CrossRef  MathSciNet  Google Scholar 

  22. R. E. Greene and S. G. Krantz, The automorphism groups of strongly pseudoconvex domains, Math. Ann. 261(1982), 425–446.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. R. E. Greene and S. G. Krantz, Stability of the Caratheodory and Kobayashi metrics and applications to biholomorphic mappings, in Complex Analysis of Several Variables, Proc. Symp. Pure Math. 41, Amer. Math. Soc., Providence, 1984.

    Google Scholar 

  24. R. E. Greene and S. G. Krantz, Characterization of complex manifolds by the isotropy subgroups of their automorphism groups, Indiana Univ. Math. Jour. 34(1985), 865–879.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. R. E. Greene and S. G. Krantz, Characterization of certain weakly pseudoconvex domains with non-compact automorphism groups, Proceedings of the Complex Analysis Week at Penn State, Springer Verlag, to appear.

    Google Scholar 

  26. R.E. Greene and S. G. Krantz, Normal families and the semicontinuity of isometry and automorphism groups, Math. Z. 190(1985), 455–567.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. R. E. Greene and S. G. Krantz, A new invariant metric in complex analysis and some applications, to appear.

    Google Scholar 

  28. M. Heins, On the number of 1–1 directly conformal maps which a multiply-connected plane region of finite connectivity p(>2) admits onto itself, Bull. Am. Math. Soc. 52(1946), 454–457.

    CrossRef  MathSciNet  MATH  Google Scholar 

  29. S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962.

    MATH  Google Scholar 

  30. L. Hörmander, Introduction to Complex Analysis in Several Variables, North Holland, Amsterdam, 1973.

    MATH  Google Scholar 

  31. L. K. Hua, Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, Am. Math. Soc., Providence, 1963.

    Google Scholar 

  32. A. Huckleberry and E. Oeljeklaus, Classifications Theorems for Almost Homogeneous Spaces. Institut Elie Cartan, Equipe Associée au C.N.R.S., no 839.

    Google Scholar 

  33. N. Kerzman and J. P. Rosay, Fonctions plurisousharmoniques d’exhaustion borneeé et domains taut, Math. Ann. 257(1981), 171–184.

    CrossRef  MathSciNet  MATH  Google Scholar 

  34. P. Klembeck, Kähler metrics of negative curvature, the Bergman metric near the boundary, and the Kobayashi metric on smooth bounded strictly pseudoconvex sets, Indiana Univ. Math. J. 27(1978), 275–282.

    CrossRef  MathSciNet  MATH  Google Scholar 

  35. J. J. Kohn, Boundary behavior of \(\bar \partial\) on weakly pseudoconvex manifolds of dimension two, J. Diff. Geom. 6(1972), 523–542.

    MathSciNet  Google Scholar 

  36. S. Krantz, Function Theory of Several Complex Variables, John Wiley and Sons, New York, 1982.

    MATH  Google Scholar 

  37. S. Krantz, Integral formulas in complex analysis, The Beijing Lectures, Ann. of Math. Studies, Princeton, 1986.

    Google Scholar 

  38. L. Lempert, Intrinsic distances and holomorphic retracts, Complex Analysis and Applications 81(1984), 341–364.

    MathSciNet  MATH  Google Scholar 

  39. E. Ligocka, preprint.

    Google Scholar 

  40. Lu Qi-Keng, On Kähler manifolds with constant curvature, Acta. Math. Sinica 16(1966), 269–281, (Chinese); (= Chinese Math. 9(1966), 283–298.)

    Google Scholar 

  41. D. Montgomery and L. Zippin, Topological Transformation Groups, Interscience, New York, 1955.

    MATH  Google Scholar 

  42. A. Morimoto and T. Nagano, On pseudo-conformal transformations of hypersurfaces, J. Math. Japan 15 (1963), 289–300.

    CrossRef  MathSciNet  MATH  Google Scholar 

  43. R. Narasimhan, Several Complex Variables, University of Chicago Press, Chicago, 1971.

    MATH  Google Scholar 

  44. G. Patrizio, Characterization of strongly convex domains biholomorphic to a circular domain, Bull. Am. Math. Soc. 9(1983), 231–233.

    CrossRef  MathSciNet  MATH  Google Scholar 

  45. J. P. Rosay, Sur une characterization de la boule parmi les domains de ℂn par son groupe d’automorphismes, Ann. Inst. Four. Grenoble XXIX(1979), 91–97.

    CrossRef  MathSciNet  MATH  Google Scholar 

  46. W. Rudin, Function Theory in the Unit Ball ofn, Springer Verlag, New York, 1980.

    CrossRef  Google Scholar 

  47. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Space, Princeton University Press, Princeton, 1971.

    MATH  Google Scholar 

  48. T. Sunada, Holomoprhic equivalence problems for bounded Reinhardt domains, Math. Ann. 235 (1978), 111–128.

    CrossRef  MathSciNet  MATH  Google Scholar 

  49. N. Suita and A. Yamada, On the Lu Qi-Keng conjecture, Proc. Am. Math. Soc. 50(1976), 222–294.

    CrossRef  MathSciNet  MATH  Google Scholar 

  50. N. Tanaka, On generalized graded Lie algebras and geometric structures I, J. Math. Soc. Japan 19(1967), 215–254.

    CrossRef  MathSciNet  MATH  Google Scholar 

  51. Bun Wong, Characterizations of the ball in ℂn by its automorphism group, Invent. Math. 41(1977), 253–257.

    CrossRef  MathSciNet  Google Scholar 

  52. H. H. Wu, Normal families of holomorphic mappings, Acta Math. 119(1967), 193–233.

    CrossRef  MathSciNet  MATH  Google Scholar 

  53. P. Yang, Automorphisms of tube domains, Am. Jour. Math. 104 (1982), 1005–1024.

    CrossRef  MATH  Google Scholar 

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© 1987 Springer-Verlag

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Greene, R.E., Krantz, S.G. (1987). Biholomorphic self-maps of domains. In: Berenstein, C.A. (eds) Complex Analysis II. Lecture Notes in Mathematics, vol 1276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078959

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  • DOI: https://doi.org/10.1007/BFb0078959

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