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On discrete Möbius groups in all dimensions: A generalization of Jørgensen's inequality

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Acta Mathematica

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References

  • [Ah]Ahlfors, L. V.,Möbius transformations in several dimensions. Lecture notes in Mathematics, University of Minnesota, 1981.

  • [Be]Beardon, A.,The Geometry of Discrete Groups. Springer Verlag, 1982.

  • [B.K.]Buser, P. & Karcher, H.,Gromov's Almost Flat Manifolds. Astérisque 81, 1981.

  • [BGS]Ballman, W., Gromov, M. & Schroeder, V.,Manifolds of Nonpositive Curvature. Progress in Mathematics, Vol. 61. Birkhäuser, 1985.

  • [Ch]Chuchrow, V., On Schottky groups with application to Kleinian groups.Ann of Math., 88 (1968), 47–61.

    Article  MathSciNet  Google Scholar 

  • [G.M.1]Gehring, F. W. &Martin, G. J., Discrete quasiconformal groups I.Proc. London Math. Soc. (3), 55 (1987), 331–358.

    MathSciNet  MATH  Google Scholar 

  • [G.M.2]-— Iteration theory and inequalities for Kleinian groups.Bull. Amer. Math. Soc., 21 (1989), 57–65.

    Article  MathSciNet  MATH  Google Scholar 

  • [G.M.3]Gehring, F. W. & Martin, G. J., Inequalities for Möbius transformations and discrete groups. To appear.

  • [Jø]Jørgensen, T., On discrete groups of Möbius transformations.Amer. J. Math., 98 (1976), 739–749.

    MATH  MathSciNet  Google Scholar 

  • [J.K.]Jørgensen, T. &Klein, P., Algebraic convergence of finitely generated Kleinian groups.Quart. J. Math. Oxford (2), 33 (1982), 325-332.

    Google Scholar 

  • [J.M.]Jørgensen, T., & Marden, A., Algebraic and geometric convergence of Kleinian groups. To appear.

  • [Ku]Kuratowski, K.,Topology. Academic Press, 1966.

  • [Ma]Marden, A., The geometry of finitely generated Kleinian groups.Ann. of Math., 99 (1974), 383–462.

    Article  MATH  MathSciNet  Google Scholar 

  • [Mar]Martin, G. J., Balls in hyperbolic manifolds. To appear inJ. London Math. Soc.

  • [Ne]Newman, M. H. A., A theorem on periodic transformation of spaces.Quart. J. Math. Oxford, 2 (1931), 1–8.

    MATH  Google Scholar 

  • [Ra]Raghunathan, M. S.,Discrete Subgroups of Lie Groups. Ergebnisse, der Mathematik, Vol. 68. Springer-Verlag, 1972.

  • [Sc]Scott, G. P., Finitely generated 3-manifold groups are finitely presented.J. London Math. Soc., 6 (1973), 437–440.

    MATH  MathSciNet  Google Scholar 

  • [Se]Selberg, A., On discontinuous groups in higher dimensional symmetric spaces.Contribution to Function Theory. Bombay, 1960, pp. 147–164.

  • [Tu]Tukia, P., On isomorphisms of geometrically finite Möbius groups.Inst. Hautes Études Sci. Publ. Math., 61 (1985), 171–214.

    MATH  MathSciNet  Google Scholar 

  • [We]Weilenberg, N., Discrete Möbius groups: Fundamental polyhedra and convergence.Amer. J. Math., 99 (1977), 861–867.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Yale University, New Haven, Connecticut, USA

    G. J. Martin

  2. The University of Auckland, Auckland, New Zealand

    G. J. Martin

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  1. G. J. Martin
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Research supported in part by a grant from the U.S. National Science Foundation.

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Martin, G.J. On discrete Möbius groups in all dimensions: A generalization of Jørgensen's inequality. Acta Math. 163, 253–289 (1989). https://doi.org/10.1007/BF02392737

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  • DOI: https://doi.org/10.1007/BF02392737

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