Acta Mathematica

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

G. J. Martin

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Note

Research supported in part by a grant from the U.S. National Science Foundation.

Article information

Source
Acta Math., Volume 163 (1989), 253-289.

Dates
Received: 17 November 1988
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485890583

Digital Object Identifier
doi:10.1007/BF02392737

Mathematical Reviews number (MathSciNet)
MR1032075

Zentralblatt MATH identifier
0698.20037

Rights
1989 © Almqvist & Wiksell

Citation

Martin, G. J. On discrete Möbius groups in all dimensions: A generalization of Jørgensen's inequality. Acta Math. 163 (1989), 253--289. doi:10.1007/BF02392737. https://projecteuclid.org/euclid.acta/1485890583


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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.
  • [G.M.1] Gehring, F. W. & Martin, G. J., Discrete quasiconformal groups I. Proc. London Math. Soc. (3), 55 (1987), 331–358.
  • [G.M.2]-— Iteration theory and inequalities for Kleinian groups. Bull. Amer. Math. Soc., 21 (1989), 57–65.
  • [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.
  • [J.K.] Jørgensen, T. & Klein, P., Algebraic convergence of finitely generated Kleinian groups. Quart. J. Math. Oxford (2), 33 (1982), 325-332.
  • [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.
  • [Mar] Martin, G. J., Balls in hyperbolic manifolds. To appear in J. London Math. Soc.
  • [Ne] Newman, M. H. A., A theorem on periodic transformation of spaces. Quart. J. Math. Oxford, 2 (1931), 1–8.
  • [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.
  • [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.
  • [We] Weilenberg, N., Discrete Möbius groups: Fundamental polyhedra and convergence. Amer. J. Math., 99 (1977), 861–867.