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International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 934295, 7 pages
http://dx.doi.org/10.1155/2012/934295
Research Article

Semicontinuity of the Automorphism Groups of Domains with Rough Boundary

Department of Mathematics, Washington University in St. Louis, St. Louis, MO 63130, USA

Received 14 August 2012; Accepted 15 October 2012

Academic Editor: Palle E. Jorgensen

Copyright © 2012 Steven G. Krantz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. E. Greene and S. G. Krantz, “The automorphism groups of strongly pseudoconvex domains,” Mathematische Annalen, vol. 261, no. 4, pp. 425–446, 1982. View at Publisher · View at Google Scholar · View at Scopus
  2. S. G. Krantz, Function Theory of Several Complex Variables, American Mathematical Society, Providenc, RI, USA, 2nd edition, 2001.
  3. R. E. Greene and S. G. Krantz, “Deformation of complex structures, estimates for the ¯-equation, and stability of the Bergman kernel,” Advances in Mathematics, vol. 43, no. 1, pp. 1–86, 1982. View at Scopus
  4. Y. W. Kim, “Semicontinuity of compact group actions on compact differentiable manifolds,” Archiv der Mathematik, vol. 49, no. 5, pp. 450–455, 1987. View at Publisher · View at Google Scholar · View at Scopus
  5. R. E. Greene and S. G. Krantz, “Normal families and the semicontinuity of isometry and automorphism groups,” Mathematische Zeitschrift, vol. 190, no. 4, pp. 455–467, 1985. View at Publisher · View at Google Scholar · View at Scopus
  6. R. E. Greene, K.-T. Kim, S. G. Krantz, and A.-R. Seo, “Semi-continuity of automorphism groups of strongly pseudoconvex domains: the low differentiability case,” The Pacific Journal of Mathematics, In press.
  7. S. G. Krantz, “Convergence of automorphisms and semicontinuity of automorphism groups,” Real Analysis Exchange. In press.
  8. S. G. Krantz and H. R. Parks, The Geometry of Domains in Space, Birkhäuser, Boston, Mass, USA, 1996.
  9. G. M. Henkin and J. Leiterer, “Theory of Functions on Strictly Pseudoconvex Sets with Nonsmooth Boundary, with German and Russian summaries,” Report MATH 1981, Akademie der Wissenschaften der DDR, Institut für Mathematik, Berlin, Germany, 1981.
  10. L. Lempert and L. Rubel, “An independence result in several complex variables,” Proceedings of the American Mathematical Society, vol. 113, pp. 1055–1065, 1991.
  11. W. Rudin, Function Theory in the Unit Ball of n, Springer, New York, NY, USA, 1980.
  12. S. G. Krantz, Cornerstones of Geometric Function Theory: Explorations in Complex Analysis, Birkhäuser, Boston, Mass, USA, 2006.
  13. B. Maskit, “The conformal group of a plane domain,” American Journal of Mathematics, vol. 90, pp. 718–722, 1968.
  14. J.-P. Rosay, “Sur une characterization de la boule parmi les domains de n par son groupe d’automorphismes,” Annales de l'institut Fourier Grenoble, vol. 29, pp. 91–97, 1979.
  15. B. Wong, “Characterization of the unit ball in n by its automorphism group,” Inventiones Mathematicae, vol. 41, no. 3, pp. 253–257, 1977. View at Publisher · View at Google Scholar · View at Scopus
  16. S. G. Krantz, “Characterizations of smooth domains in by their biholomorphic self maps,” American Mathematical Monthly, vol. 90, pp. 555–557, 1983.
  17. G. Julia, “Leçons sur la représentation conforme des aires multiplement connexes,” Paris, France, 1934.
  18. M. Heins, “On the number of 1-1 directly conformal maps which a multiply-connected plane regions of finite connectivity p(>2) admits onto itself,” Bulletin of the AMS, vol. 52, pp. 454–457, 1946.
  19. L. Apfel, Localization properties and boundary behavior of the Bergman kernel [thesis], Washington University in St. Louis, 2003.