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The noncompact hyperbolic $ 3$-manifold of minimal volume


Author: Colin C. Adams
Journal: Proc. Amer. Math. Soc. 100 (1987), 601-606
MSC: Primary 57N10; Secondary 20H10, 57M10, 57M25
DOI: https://doi.org/10.1090/S0002-9939-1987-0894423-8
MathSciNet review: 894423
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Abstract: We utilize maximal cusp volumes in order to prove that the Gieseking manifold is the unique complete noncompact hyperbolic $ 3$-manifold of minimal hyperbolic volume.


References [Enhancements On Off] (What's this?)

  • [1] C. Adams, Volumes of $ N$-cusp hyperbolic $ 3$-manifolds, preprint.
  • [2] C. Adams, M. Hildebrand and J. Weeks, Hyperbolic invariants of knot and link complements (in preparation).
  • [3] A. Beardon, The geometry of discrete groups, Springer-Verlag, Berlin and New York, 1983. MR 698777 (85d:22026)
  • [4] K. Boroczky, Packing of spheres in spaces of constant curvature, Acta Math. Acad. Sci. Hungar. 32 (1978), 243-326. MR 512399 (80h:52014)
  • [5] H. Gieseking, Analytische Untersuchungen über Topologische Gruppen, Thesis, Muenster, 1912.
  • [6] R. Meyerhoff, Sphere packing and volume in hyperbolic $ 3$-space, Comment. Math Helv. 61 (1986), 271-278. MR 856090 (88e:52023)
  • [7] -, The cusped hyperbolic $ 3$-orbifold of minimum volume, Bull. Amer. Math. Soc. (N.S.) 13 (1985), 154-156. MR 799800 (87b:22022)
  • [8] -, A lower bound for the volume of hyperbolic $ 3$-manifolds, Canad J. Math. (to appear).
  • [9] J. Milnor, Hyperbolic geometry: the first 150 years, Bull. Amer. Math. Soc. (N.S.) 6 (1982), 9-23. MR 634431 (82m:57005)
  • [10] W. Thurston, The geometry and topology of $ 3$-manifolds, class notes, Princeton University, 1978.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0894423-8
Keywords: Hyperbolic $ 3$-manifold, hyperbolic volume, Gieseking manifold
Article copyright: © Copyright 1987 American Mathematical Society

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