Skip to main content
SpringerLink
Log in

Discreteness criteria in PU (1, n; C)

  • Published:
Proceedings - Mathematical Sciences Aims and scope Submit manuscript

Abstract

In this paper, we study the discreteness for non-elementary subgroups in PU (1, n; C), and several discreteness criteria are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abikoff W and Hass A, Nondiscrete groups of hyperbolic motions, Bull. London Math. Soc. 22 (1990) 233–238

    Article  MATH  MathSciNet  Google Scholar 

  2. Chen S and Greenberg L, Hyperbolic spaces, Contributions to analysis (New York: Academic Press) (1974) pp. 49–87

    Google Scholar 

  3. Cao W and Wang X, Discreteness criteria and algebraic convergence theorem in PU (1, n; C), Proc. Japan Acad. A82 (2006) 49–52

    MathSciNet  Google Scholar 

  4. Dai B, Fang A and Nai B, Discreteness criteria for subgroups in complex hyperbolic space, Proc. Japan Acad. 77 (2001) 168–172

    Article  MATH  MathSciNet  Google Scholar 

  5. Fang A and Nai B, On the discreteness and convergence in n-dimensional Möbius groups, J. London Math. Soc. 61 (2000) 761–773

    Article  MATH  MathSciNet  Google Scholar 

  6. Gilman J, Inequalities in discrete subgroup of PSL(2, R), Canad. J. Math. 40 (1988) 115–130

    MATH  MathSciNet  Google Scholar 

  7. Goldman W M, Complex hyperbolic geometry (Oxford: Oxford University Press) (1999)

    MATH  Google Scholar 

  8. Isachenko N A, Systems of generators of subgroup of PSL(2, C), Siberian Math. J. 31 (1990) 162–165

    Article  MATH  MathSciNet  Google Scholar 

  9. Jiang Y P, On the discreteness of Möbius groups of high dimensions, Math. Proc. Cambridge Philos. Soc. 136 (2004) 547–555

    Article  MATH  MathSciNet  Google Scholar 

  10. Jørgensen T, On discrete groups of Möbius transformations, Am. J. Math. 98 (1976) 739–749

    Article  Google Scholar 

  11. Jørgensen T, A note on subgroup of SL(2,C), Quart. J. Math. Oxford 33 (1982) 325–332

    Article  Google Scholar 

  12. Kamiya S, Chordal and matrix norms of unitary transformations, First Korean-Japanese Colloquium on finite or infinite dimensional complex analysis (eds) J Kajiwara, H Kazama and K H Shon (1993) pp. 121–125

  13. Martin G J, On discrete Möbius groups in all dimensions, Acta Math. 163 (1989) 253–289

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Hunan University, Changsha, 410082, People’s Republic of China

    Hua Wang & Yueping Jiang

  2. Department of Mathematics, Changsha University of Science and Technology, Changsha, 410072, People’s Republic of China

    Hua Wang

Authors
  1. Hua Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yueping Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hua Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, H., Jiang, Y. Discreteness criteria in PU (1, n; C). Proc Math Sci 120, 243–248 (2010). https://doi.org/10.1007/s12044-010-0015-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12044-010-0015-2

Keywords

Search

Navigation