Mathematische Annalen

, Volume 261, Issue 4, pp 425–446

The automorphism groups of strongly pseudoconvex domains

  • Robert E. Greene
  • Steven G. Krantz
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bell, S.: Biholomorphic mappings and the\(\bar \partial\) problem. Ann. Math.114, 103–112 (1981)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)CrossRefGoogle Scholar
  3. 3.
    Bergman, S.: Über die Existenz von Repräsentantenbereichen. Math. Ann.102, 430–446 (1929)Google Scholar
  4. 4.
    Bochner, S., Martin, W.T.: Several complex variables. Princeton: Princeton University Press 1948Google Scholar
  5. 5.
    Bochner, S., Montgomery, D.: Groups on analytic manifolds. Ann. Math.48, 659–669 (1947)Google Scholar
  6. 6.
    Burns, D., Shnider, S., Wells, R.O.: On deformations of strictly pseudoconvex domains. Invent. Math.46, 237–253 (1978)Google Scholar
  7. 7.
    Chern, S., Moser, J.: Real hypersurfaces in complex manifolds. Acta Math.133, 219–271 (1974)Google Scholar
  8. 8.
    Ebin, D.: The manifold of Riemannian metric. Proceedings of Symposia in Pure Mathematics, Vol. XV (Global Analysis), A.M.S. pp. 11–40 (1970)Google Scholar
  9. 9.
    Fefferman, C.: The Bergman kernel and biholomorphic mappings of pseudonvex domains. Invent. Math.26, 1–65 (1974)Google Scholar
  10. 10.
    Floyd, E.E., Richardson, R.W.: An action of a finite group on ann-cell without stationary points. Bull. Am. Math. Soc.65, 73–76 (1959)Google Scholar
  11. 11.
    Fuks, B.A.: Special chapters in the theory of analytic functions of several complex variables. Providence: American Mathematical Society 1965Google Scholar
  12. 12.
    Greene, R., Krantz, S.: The stability of the Bergman kernel and the geometry of the Bergman metric. Bull. Am. Math. Soc.4, 111–115 (1981)Google Scholar
  13. 13.
    Greene, R.E., Krantz, S.G.: Stability of the Bergman kernel and curvature properties of bounded domains. In: Recent developments in several complex variables. J. Fornaess, ed., Annals of Math. Studies No. 100. Princeton: Princeton University Press 1981Google Scholar
  14. 14.
    Greene, R.E., Krantz, S.: Deformations of complex structures, estimates for the\(\bar \partial\) equation, and stability of the Bergman kernel. Adv. Math.43, 1–86 (1982)Google Scholar
  15. 15.
    Helgason, S.: Differential geometry and symmetric spaces. New York: Academic Press 1962Google Scholar
  16. 16.
    Hörmander, L.: Linear partial differential operators. Berlin, Göttingen, Heidelberg: Springer 1963Google Scholar
  17. 17.
    Katznelson, Y.: Introduction to harmonic analysis. New York: Wiley 1968Google Scholar
  18. 18.
    Kerzman, N.: The Bergman kernel function: differentiability at the boundary. Math. Ann.195, 149–158 (1972)Google Scholar
  19. 19.
    Klembeck, P.: 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, 275–282 (1978)Google Scholar
  20. 20.
    Kobayashi, S.: Transformation groups in differential geometry. Berlin, Heidelberg, New York: Springer 1972Google Scholar
  21. 21.
    Kobayashi, S., Nomizu, K.: Foundations of differential geometry, Vol. II. New York: Wiley 1969Google Scholar
  22. 22.
    Lewy, H.: On the boundary behavior of holomorphic mappings. Acad. Naz. Lincei35, 1–8 (1977)Google Scholar
  23. 23.
    Lu Qi-Keng: On Kähler manifolds with constant curvature. Acta Math. Sinica16, 269–281 (1966) (in Chinese). Engl. Transl. Look, K.H.: Chinese Math.9, 283–298 (1966)Google Scholar
  24. 24.
    Munkres, J.: Elementary differential topology. Princeton: Princeton University Press 1963Google Scholar
  25. 25.
    Palais, R.: Foundations of global non-linear analysis. New York: Benjamin 1968Google Scholar
  26. 26.
    Pincuk, S.: On the analytic continuations of holomorphic mappings. Mat. Sb.98, 375–392 (1975); Mat. USSR Sb.27, 416–435 (1975)Google Scholar
  27. 27.
    Rosay, J.P.: Sur une characterization de la boule parmi les domains deC n par son groupe d'automorphismes. Ann. Inst. Fourier Grenoble29, 91–97 (1979)Google Scholar
  28. 28.
    Stein, E.M.: Boundary behavior of holomorphic functions of several complex variables. Princeton: Princeton University Press: 1972Google Scholar
  29. 29.
    Tanaka, N.: On generalized graded Lie algebras and geometric structures. I. J. Math. Soc. Japan19, 215–254 (1967)Google Scholar
  30. 30.
    Webster, S.: Biholomorphic mappings and the Bergman kernel off the diagonal. Invent. Math.51, 155–169 (1979)Google Scholar
  31. 31.
    Wong, B.: Characterization of the unit ball inC n by its automorphism group. Invent. Math.41, 253–257 (1977)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Robert E. Greene
    • 1
  • Steven G. Krantz
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

Personalised recommendations