Duke Mathematical Journal

Geometrical finiteness with variable negative curvature

B. H. Bowditch

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Article information

Source
Duke Math. J. Volume 77, Number 1 (1995), 229-274.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077286152

Mathematical Reviews number (MathSciNet)
MR1317633

Zentralblatt MATH identifier
0877.57018

Digital Object Identifier
doi:10.1215/S0012-7094-95-07709-6

Subjects
Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
Secondary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20] 57R99: None of the above, but in this section

Citation

Bowditch, B. H. Geometrical finiteness with variable negative curvature. Duke Math. J. 77 (1995), no. 1, 229--274. doi:10.1215/S0012-7094-95-07709-6. http://projecteuclid.org/euclid.dmj/1077286152.


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References

  • [Ah] L. V. Ahlfors, Fundamental polyhedrons and limit point sets of Kleinian groups, Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 251–254.
  • [An] M. Anderson, The Dirichlet problem at infinity for manifolds of negative curvature, J. Differential Geom. 18 (1983), no. 4, 701–721.
  • [BaGS] W. Ballmann, M. Gromov, and V. Schroeder, Manifolds of Nonpositive Curvature, Progr. Math., vol. 61, Birkhäuser, Boston, 1985.
  • [BeM] A. Beardon and B. Maskit, Limit points of Kleinian groups and finite sided fundamental polyhedra, Acta Math. 132 (1974), 1–12.
  • [Bo1] B. H. Bowditch, Geometrical finiteness for hyperbolic groups, J. Funct. Anal. 113 (1993), no. 2, 245–317.
  • [Bo2] B. H. Bowditch, Discrete parabolic groups, J. Differential Geom. 38 (1993), no. 3, 559–583.
  • [Bo3] B. H. Bowditch, Some results on the geometry of convex hulls in manifolds of pinched negative curvature, Comment. Math. Helv. 69 (1994), no. 1, 49–81.
  • [Br] M. R. Bridson, Geodesics and curvature in metric simplicial complexes, Group Theory from a Geometrical Viewpoint (Trieste, 1990) eds. E. Ghys, A. Haefliger, and A. Verjovsky, World Scientific, River Edge, NJ, 1991, pp. 373–463.
  • [CE] J. Cheeger and D. G. Ebin, Comparison Theorems in Riemannian Geometry, North-Holland Math. Lib., vol. 9, North-Holland, Amsterdam, 1975.
  • [EM] D. B. A. Epstein and A. Marden, Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces, Analytical and Geometric Aspects of Hyperbolic Space (Coventry/Durham, 1984) ed. D. B. A. Epstein, London Math. Soc. Lecture Note Series, vol. 111, Cambridge Univ. Press, Cambridge, 1987, pp. 113–253.
  • [G] W. M. Goldman, Complex hyperbolic Kleinian groups, Complex Geometry (Osaka, 1990), Lecture Notes in Pure and Appl. Math., vol. 143, Dekker, New York, 1993, pp. 31–52.
  • [GP] W. M. Goldman and J. R. Parker, On the horospherical geometry of complex hyperbolic space, preprint, Univ. of Maryland, 1991.
  • [HI] E. Heintze and H. C. Im Hof, Geometry of horospheres, J. Differential Geom. 12 (1977), no. 4, 481–491.
  • [M] A. Marden, The geometry of finitely generated kleinian groups, Ann. of Math. (2) 99 (1974), 383–462.
  • [Pa] J. R. Parker, Dirichlet polyhedra for parabolic cyclic groups acting on complex hyperbolic space, preprint, Warwick Univ., 1992.
  • [Ph] M. B. Phillips, Dirichlet polyhedra for cyclic groups in complex hyperbolic space, Proc. Amer. Math. Soc. 115 (1992), no. 1, 221–228.
  • [S] M. Spivak, A Comprehensive Introduction to Differential Geometry, 2nd ed., Publish or Perish, Wilmington, Del., 1979.
  • [T] W. P. Thurston, The geometry and topology of $3$-manifold, Princeton Univ., Department of Mathematics, 1979.