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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 638638, 5 pages
http://dx.doi.org/10.1155/2013/638638
Research Article

Discreteness and Convergence of Complex Hyperbolic Isometry Groups

Department of Mathematics, Shaoxing University, Shaoxing, Zhejiang 312000, China

Received 10 June 2013; Accepted 2 October 2013

Academic Editor: Pedro M. Lima

Copyright © 2013 Xi Fu. 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. T. Jørgensen, “On discrete groups of Möbius transformation,” American Journal of Mathematics, vol. 98, pp. 739–749, 1976.
  2. T. Jørgensen, “A note on subgroups of SL(2,),” The Quarterly Journal of Mathematics, vol. 28, no. 110, pp. 209–211, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. J. Gilman, “Inequalities in discrete subgroups of PSL (2,),” Canadian Journal of Mathematics, vol. 40, no. 1, pp. 115–130, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. N. A. Isachenko, “Systems of generators of subgroups of PSL (2,),” Siberian Mathematical Journal, vol. 31, no. 1, pp. 162–165, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. F. Beardon, The Geometry of Discrete Groups, vol. 91 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  6. P. Tukia and X. Wang, “Discreteness of subgroups of SL (2,) containing elliptic elements,” Mathematica Scandinavica, vol. 91, no. 2, pp. 214–220, 2002. View at Zentralblatt MATH · View at MathSciNet
  7. X. Wang and W. Yang, “Discreteness criterions for subgroups in SL (2,),” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 124, no. 1, pp. 51–55, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  8. S. Yang, “Test maps and discrete groups in SL (2,),” Osaka Journal of Mathematics, vol. 46, no. 2, pp. 403–409, 2009. View at Zentralblatt MATH · View at MathSciNet
  9. W. Abikoff and A. Haas, “Nondiscrete groups of hyperbolic motions,” The Bulletin of the London Mathematical Society, vol. 22, no. 3, pp. 233–238, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. Chen, “Discreteness and convergence of Möbius groups,” Geometriae Dedicata, vol. 104, pp. 61–69, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. A. Fang and B. Nai, “On the discreteness and convergence in n-dimensional Möbius groups,” Journal of the London Mathematical Society, vol. 61, no. 3, pp. 761–773, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  12. G. J. Martin, “On discrete Möbius groups in all dimensions: a generalization of Jørgensen's inequality,” Acta Mathematica, vol. 163, no. 3-4, pp. 253–289, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. X. Wang and W. Yang, “Discreteness criteria of Möbius groups of high dimensions and convergence theorems of Kleinian groups,” Advances in Mathematics, vol. 159, no. 1, pp. 68–82, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. X. Wang, L. Li, and W. Cao, “Discreteness criteria for Möbius groups acting on n¯,” Israel Journal of Mathematics, vol. 150, pp. 357–368, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. S. S. Chen and L. Greenberg, “Hyperbolic spaces,” in Contributions to Analysis a Collection of Papers Dedicated to Lipman Bers, pp. 49–87, Academic Press, New York, NY, USA, 1974. View at Zentralblatt MATH · View at MathSciNet
  16. H. Qin and Y. Jiang, “Discreteness criteria based on a test map in PU(n,1),” Proceedings—Mathematical Sciences, vol. 122, no. 4, pp. 519–524, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. X. Wang, “Algebraic convergence theorems of n-dimensional Kleinian groups,” Israel Journal of Mathematics, vol. 162, pp. 221–233, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  18. W. Cao, “Algebraic convergence theorems of complex Kleinian groups,” Glasgow Mathematical Journal, vol. 55, no. 1, pp. 1–8, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. W. M. Goldman, Complex Hyperbolic Geometry, Oxford University Press, Oxford, UK, 1999. View at MathSciNet
  20. B. Dai, A. Fang, and B. Nai, “Discreteness criteria for subgroups in complex hyperbolic space,” Proceedings of the Japan Academy, vol. 77, no. 10, pp. 168–172, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. M. Kapovich, “On sequences of finitely generated discrete groups,” in In the Tradition of Ahlfors-Bers. V, vol. 510 of Contemporary Mathematics, pp. 165–184, American Mathematical Society, Providence, RI, USA, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet