Inventiones mathematicae

, Volume 146, Issue 3, pp 451–478

The orientable cusped hyperbolic 3-manifolds of minimum volume

  • Chun Cao
  • G. Robert Meyerhoff


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

c++programs.htm (4 kb)
Supplementary material
affApprox.cxx.txt (4 kb)
Supplementary material
affApprox.h.txt (1 kb)
Supplementary material
aHWkill.cxx.txt (3 kb)
Supplementary material
distcalcs.cxx.txt (6 kb)
Supplementary material
distcalcs.h.txt (1 kb)
Supplementary material
m_AffApprox_cxx.txt (6 kb)
Supplementary material
m_AffApprox_h.txt (1 kb)
Supplementary material
makefileAHW.txt (0 kb)
Supplementary material
makefileNoF.txt (0 kb)
Supplementary material
myDouble.cxx.txt (4 kb)
Supplementary material
myDouble.h.txt (1 kb)
Supplementary material
noFSBs2.cxx.txt (2 kb)
Supplementary material
NoFSBs2_cxx.txt (2 kb)
Supplementary material
s_AffApprox_cxx.txt (6 kb)
Supplementary material
s_AffApprox_h.txt (1 kb)
Supplementary material
seen.cxx.txt (2 kb)
Supplementary material
seen.h.txt (0 kb)
Supplementary material
AHWKill.tar.gz (4 kb)
Supplementary material
Min1.05.tar.gz (4 kb)
Supplementary material
SeenArea.tar.gz (4 kb)
Supplementary material
AHWexamples.htm (1 kb)
Supplementary material
Min1.htm (1 kb)
Supplementary material
SeenArea.htm (2 kb)
Supplementary material


  1. 1.
    C. Adams, The non-compact hyperbolic 3-manifold of minimum volume, Proc. AMS, 100 (1987), 601–606MATHCrossRefGoogle Scholar
  2. 2.
    C. Adams, Limit volumes of hyperbolic 3-orbifolds, J. Diff. Geometry 34(1991), 115–141MATHGoogle Scholar
  3. 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, 1992Google Scholar
  4. 4.
    C. Adams, Waist size for cusps in hyperbolic 3-manifolds, to appear, TopologyGoogle Scholar
  5. 5.
    C. Adams, D. Biddle, C. Gwosdz, K.A. Paur, S. Reynolds, Minimal Volume Maximal Cusps in Hyperbolic 3-Manifolds, in preparationGoogle Scholar
  6. 6.
    C. Adams, M. Hildebrand, J. Weeks, Hyperbolic invariants of knots and links, Trans. AMS 326 (1991), 1–56MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    A. Beardon, The Geometry of discrete groups, Springer-Verlag, New York, 1983MATHGoogle Scholar
  8. 8.
    K. Böröczky, Packings of spheres in spaces of constant curvature, Acta Math. Acad. Sci. Hungar. 32 (1978), 243–261MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    J. Conway, N. Sloane, Sphere packings, lattices and codes, Springer-Verlag, New York, 1988 (1st edition)Google Scholar
  10. 10.
    L.R. Ford, Automorphic functions, Chelsea, New York, 1951 (2nd edition)MATHGoogle Scholar
  11. 11.
    D. Gabai, G.R. Meyerhoff, N. Thurston, Homotopy hyperbolic 3-manifolds are hyperbolic, to appear, Annals of Math.Google Scholar
  12. 12.
    F.W. Gehring, G.J. Martin, Commutators, collars and the geometry of Möbius groups, J. D'Analyse Math. 63 (1994), 175–219MATHMathSciNetCrossRefGoogle Scholar
  13. 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, 1985Google Scholar
  14. 14.
    O. Lanford, Computer-Assisted Proofs in Analysis, in: Proceedings of the ICM, Berkeley, California, 1986, vol. 2, 1385–1394Google Scholar
  15. 15.
    G.R. Meyerhoff, A lower bound for the volume of hyperbolic 3-manifolds, Canadian J. Math. 39 (1987), 1038–1056MATHMathSciNetGoogle Scholar
  16. 16.
    G.R. Meyerhoff, Sphere-packing and volume in hyperbolic 3-space, Comment. Math. Helv. 61 (1986), 271–278MATHMathSciNetGoogle Scholar
  17. 17.
    G.D. Mostow, Strong rigidity of locally symmetric spaces, Princeton Univ. Press, Princeton, 1973MATHGoogle Scholar
  18. 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, 1979Google Scholar
  19. 19.
    W.P. Thurston, The geometry and topology of 3-manifolds, Princeton Univ. preprint, 1978Google Scholar
  20. 20.
    W.P. Thurston, The geometry and topology of 3-manifolds, Princeton Univ. Press, Princeton, 1997Google Scholar
  21. 21.
    J. Weeks, Hyperbolic structures on 3-manifolds, Princeton Univ. Ph.D. thesis, 1985Google Scholar

Copyright information

© Springer-Verlag 2001

Authors and Affiliations

  • Chun Cao
    • 1
  • G. Robert Meyerhoff
    • 2
  1. 1.David L. Babson & Co. Inc.CambridgeUSA
  2. 2.Department of MathematicsBoston CollegeChestnut HillUSA

Personalised recommendations