Skip to main content
SpringerLink
Log in

The orientable cusped hyperbolic 3-manifolds of minimum volume

  • Published:
Inventiones mathematicae Aims and scope

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. C. Adams, The non-compact hyperbolic 3-manifold of minimum volume, Proc. AMS, 100 (1987), 601–606

    Article  MATH  Google Scholar 

  2. C. Adams, Limit volumes of hyperbolic 3-orbifolds, J. Diff. Geometry 34(1991), 115–141

    MATH  Google Scholar 

  3. C. Adams, Noncompact hyperbolic 3-orbifolds of small volume, pp. 1–15 in: Topology 90, ed. B. Apanasov, W. Neumann, A. Reid, L. Siebenmann, Walter de Gruyter & Co., Berlin, 1992

    Google Scholar 

  4. C. Adams, Waist size for cusps in hyperbolic 3-manifolds, to appear, Topology

  5. C. Adams, D. Biddle, C. Gwosdz, K.A. Paur, S. Reynolds, Minimal Volume Maximal Cusps in Hyperbolic 3-Manifolds, in preparation

  6. C. Adams, M. Hildebrand, J. Weeks, Hyperbolic invariants of knots and links, Trans. AMS 326 (1991), 1–56

    Article  MATH  MathSciNet  Google Scholar 

  7. A. Beardon, The Geometry of discrete groups, Springer-Verlag, New York, 1983

    MATH  Google Scholar 

  8. K. Böröczky, Packings of spheres in spaces of constant curvature, Acta Math. Acad. Sci. Hungar. 32 (1978), 243–261

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Conway, N. Sloane, Sphere packings, lattices and codes, Springer-Verlag, New York, 1988 (1st edition)

    Google Scholar 

  10. L.R. Ford, Automorphic functions, Chelsea, New York, 1951 (2nd edition)

    MATH  Google Scholar 

  11. D. Gabai, G.R. Meyerhoff, N. Thurston, Homotopy hyperbolic 3-manifolds are hyperbolic, to appear, Annals of Math.

  12. F.W. Gehring, G.J. Martin, Commutators, collars and the geometry of Möbius groups, J. D'Analyse Math. 63 (1994), 175–219

    Article  MATH  MathSciNet  Google Scholar 

  13. IEEE Standard for Binary Floating-Point Arithmetic (ANSI/IEEE Std 754-1985) published by the Institute of Electrical and Electronics Engineers, Inc., NY, NY, 1985

  14. O. Lanford, Computer-Assisted Proofs in Analysis, in: Proceedings of the ICM, Berkeley, California, 1986, vol. 2, 1385–1394

    Google Scholar 

  15. G.R. Meyerhoff, A lower bound for the volume of hyperbolic 3-manifolds, Canadian J. Math. 39 (1987), 1038–1056

    MATH  MathSciNet  Google Scholar 

  16. G.R. Meyerhoff, Sphere-packing and volume in hyperbolic 3-space, Comment. Math. Helv. 61 (1986), 271–278

    MATH  MathSciNet  Google Scholar 

  17. G.D. Mostow, Strong rigidity of locally symmetric spaces, Princeton Univ. Press, Princeton, 1973

    MATH  Google Scholar 

  18. R. Riley, An elliptical path from parabolic representations to hyperbolic structures, in: Topology of low-dimensional manifolds, ed. R. Fenn, L.N.M., Vol. 722, Springer-Verlag, 1979

  19. W.P. Thurston, The geometry and topology of 3-manifolds, Princeton Univ. preprint, 1978

  20. W.P. Thurston, The geometry and topology of 3-manifolds, Princeton Univ. Press, Princeton, 1997

    Google Scholar 

  21. J. Weeks, Hyperbolic structures on 3-manifolds, Princeton Univ. Ph.D. thesis, 1985

Download references

Author information

Authors and Affiliations

  1. David L. Babson & Co. Inc., One Memorial Drive, 02142, Cambridge, MA, USA

    Chun Cao

  2. Department of Mathematics, Boston College, 02467, Chestnut Hill, MA, USA

    G. Robert Meyerhoff

Authors
  1. Chun Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Robert Meyerhoff
    View author publications

    You can also search for this author in PubMed Google Scholar

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cao, C., Meyerhoff, G. The orientable cusped hyperbolic 3-manifolds of minimum volume. Invent. math. 146, 451–478 (2001). https://doi.org/10.1007/s002220100167

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s002220100167

Keywords

Search

Navigation