Skip to main content
Log in

Geometrically finite hyperbolic structures on manifolds

  • Published:
Annals of Global Analysis and Geometry Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. Apanasov, B.N.: “On an analytic method in the theory of Kleinian groups on a multidimensional Euclidean space” (Russian), Dokl. Akad. Nauk SSSR, 222 (1975), no.1, pp. 11–14; (Soviet Math . Dokl., vol. 16(1975)., no. 3, pp. 553–556).

    MATH  MathSciNet  Google Scholar 

  2. Apanasov, B.N.: “A universal property of Kleinian groups in the hyperbolic metric” (Russian), Dokl. Akad. Nauk SSSR, 225 (1975), no. 1, pp. 15–18; (Soviet Math. Dokl. , vol. 16 (1975), no.6, pp. 1418–1421).

    MATH  MathSciNet  Google Scholar 

  3. Apanasov, B.N.:“Entire automorphic forms in Rn” (Russian), Sibirsk. Mat. Z., 19 (1978), no.4, pp. 735–748.

    MATH  MathSciNet  Google Scholar 

  4. Apanasov, B.N.: “Nontriviality of Teichmüller space for Kleinian group in space”, in: Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference”, Ann. of Math. Studies, no .97, Princeton, Princeton Univ . Press, 1981, pp. 21–31.

    Google Scholar 

  5. Apanasov, B.N.: “Kleinian groups, Teichmüller space, and the Mostow rigidty theorem” (Russian), Sibirsk. Mat. Z., 21 (1980), no. 4,pp. 3–20.

    MATH  MathSciNet  Google Scholar 

  6. Apanasov, B.N.: “Geometrically finite groups of space transformations” (Russian), Sibirsk. Mat. Z., 23 (1982), no.6, pp. 16–27.

    MATH  MathSciNet  Google Scholar 

  7. Apanasov, B.N.: “A criterion of geometrical finiteness of Kleinian groups in space” (Russian), Abstracts of the Intern. Conf. on Complex Analysis and Application, Varna, 1981, p. 88.

  8. Beardon, A., Maskit, B.: “Limit points of Kleinian groups and finite sided fundamental polyhedra”, Acta Math., 132 (1974), pp. 1–12.

    MathSciNet  Google Scholar 

  9. Greenberg, L.: “Fundamental polyhedra for Kleinian groups”, Ann. of Math., 84 (1966), no.3, pp. 433–442.

    MATH  MathSciNet  Google Scholar 

  10. Greenberg, L.: “Finiteness theorems for Fuchsian and Kleinian groups”, in: Discrete groups and automorphic functions, London, Akad. Press, 1977, pp. 199–257.

    Google Scholar 

  11. Hedlund, G.A.: “Fuchsian groups and transitive horocycles”, Duke Math. J., 2 (1936), pp. 530–542.

    Article  MATH  MathSciNet  Google Scholar 

  12. Margulis, G.A.: “Discrete motion groups on manifolds of nonpositive curvature” (Russian), in: Proc. of the Intern. Congress of Math., Vancouver, 2(1974), pp. 21–34.

  13. Sullivan, D.: “On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions”, in: “Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference, Ann. of Math. Studies, no. 97, Princeton, Princeton Univ. Press, 1981, pp. 465–496.

    Google Scholar 

  14. Tetenov, A.V.: “Locally finite fundamental domains of discrete groups in space” (Russian), Sibirsk. Math. Z., 23 (1982), no.6, pp. 88–99.

    MathSciNet  Google Scholar 

  15. Thurston, W.: “The geometry and topology of 3-manifolds”, preprint, Princeton University, 1978; (Princeton Math. Notes, no.28, 1982 - to appear).

  16. Thurston, W.: “Three dimensional manifolds, Kleinian groups and hyperbolic geometry”, Bull. Amer. Math. Soc. (New Series), 6 (1982), no.3, pp.357–381.

    MATH  MathSciNet  Google Scholar 

  17. Wolf, J.: “Spaces of constant curvature”, New York, McGraw-Hill 1967.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Apanasov, B.N. Geometrically finite hyperbolic structures on manifolds. Ann Glob Anal Geom 1, 1–22 (1983). https://doi.org/10.1007/BF02329729

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02329729

Keywords

Navigation