## Duke Mathematical Journal

### Degenerations of the hyperbolic space

#### Article information

Source
Duke Math. J. Volume 56, Number 1 (1988), 143-161.

Dates
First available: 20 February 2004

http://projecteuclid.org/euclid.dmj/1077306456

Mathematical Reviews number (MathSciNet)
MR932860

Zentralblatt MATH identifier
0652.57009

Digital Object Identifier
doi:10.1215/S0012-7094-88-05607-4

#### Citation

Bestvina, Mladen. Degenerations of the hyperbolic space. Duke Mathematical Journal 56 (1988), no. 1, 143--161. doi:10.1215/S0012-7094-88-05607-4. http://projecteuclid.org/euclid.dmj/1077306456.

#### References

• [Be] A. F. Beardon, The geometry of discrete groups, Graduate Texts in Mathematics, vol. 91, Springer-Verlag, New York, 1983.
• [Bo] F. Bonahon, Bouts des variétés hyperboliques de dimension $3$, Ann. of Math. (2) 124 (1986), no. 1, 71–158.
• [C-M] M. Culler and J. W. Morgan, Group actions on $\mathbbR$-trees, MSRI preprint, 1985.
• [C-S] M. Culler and P. B. Shalen, Varieties of group representations and splittings of $3$-manifolds, Ann. of Math. (2) 117 (1983), no. 1, 109–146.
• [Gr] M. Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. (1981), no. 53, 53–73.
• [Mo] G. D. Mostow, Strong rigidity of locally symmetric spaces, Annals of Mathematics Studies, vol. 78, Princeton University Press, Princeton, N.J., 1973.
• [M] J. W. Morgan, Group actions on trees and the compactification of the spaces of classes of $\mathrmSO(n,1)$-representations, preprint.
• [MS1] J. W. Morgan and P. B. Shalen, Valuations, trees, and degenerations of hyperbolic structures. I, Ann. of Math. (2) 120 (1984), no. 3, 401–476.
• [MS2] J. W. Morgan and P. B. Shalen, Degenerations of hyperbolic structures II, preprint.
• [P] F. Paulin, Topologies de Gromov équivariantes, structures hyperboliques et arbres réals, dissertation, Orsay, 1986.
• [Se] A. Selberg, On discontinuous groups in higher-dimensional symmetric spaces, Contributions to function theory (internat. Colloq. Function Theory, Bombay, 1960), Tata Institute of Fundamental Research, Bombay, 1960, pp. 147–164.
• [TH1] W. P. Thurston, Geometry and topology of $3$-manifolds, unpublished manuscript, Princeton, 1979.
• [TH2] W. P. Thurston, Hyperbolic structures on $3$-manifolds. I. Deformation of acylindrical manifolds, Ann. of Math. (2) 124 (1986), no. 2, 203–246.