On the geometric and topological rigidity of hyperbolic 3-manifolds
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- by David Gabai
- J. Amer. Math. Soc. 10 (1997), 37-74
- DOI: https://doi.org/10.1090/S0894-0347-97-00206-3
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References
- Michael T. Anderson, Complete minimal varieties in hyperbolic space, Invent. Math. 69 (1982), no. 3, 477–494. MR 679768, DOI 10.1007/BF01389365
- F. Bonahon and L. Siebenmann, to appear.
- D. B. A. Epstein and A. Marden, Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces, Analytical and geometric aspects of hyperbolic space (Coventry/Durham, 1984) London Math. Soc. Lecture Note Ser., vol. 111, Cambridge Univ. Press, Cambridge, 1987, pp. 113–253. MR 903852
- Werner Fenchel, Elementary geometry in hyperbolic space, De Gruyter Studies in Mathematics, vol. 11, Walter de Gruyter & Co., Berlin, 1989. With an editorial by Heinz Bauer. MR 1004006, DOI 10.1515/9783110849455
- M. H. Freedman and He, personal communication.
- F. T. Farrell and L. E. Jones, A topological analogue of Mostow’s rigidity theorem, J. Amer. Math. Soc. 2 (1989), no. 2, 257–370. MR 973309, DOI 10.1090/S0894-0347-1989-0973309-4
- David Gabai, Foliations and the topology of $3$-manifolds, J. Differential Geom. 18 (1983), no. 3, 445–503. MR 723813
- David Gabai, Foliations and $3$-manifolds, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990) Math. Soc. Japan, Tokyo, 1991, pp. 609–619. MR 1159248
- David Gabai, Homotopy hyperbolic $3$-manifolds are virtually hyperbolic, J. Amer. Math. Soc. 7 (1994), no. 1, 193–198. MR 1205445, DOI 10.1090/S0894-0347-1994-1205445-3
- David Gabai and Ulrich Oertel, Essential laminations in $3$-manifolds, Ann. of Math. (2) 130 (1989), no. 1, 41–73. MR 1005607, DOI 10.2307/1971476
- Michael Gromov, Hyperbolic manifolds (according to Thurston and Jørgensen), Bourbaki Seminar, Vol. 1979/80, Lecture Notes in Math., vol. 842, Springer, Berlin-New York, 1981, pp. 40–53. MR 636516
- Robert Gulliver and Peter Scott, Least area surfaces can have excess triple points, Topology 26 (1987), no. 3, 345–359. MR 899054, DOI 10.1016/0040-9383(87)90006-1
- Joel Hass and Peter Scott, The existence of least area surfaces in $3$-manifolds, Trans. Amer. Math. Soc. 310 (1988), no. 1, 87–114. MR 965747, DOI 10.1090/S0002-9947-1988-0965747-6
- J. M. Kister, Isotopies in $3$-manifolds, Trans. Amer. Math. Soc. 97 (1960), 213–224. MR 120628, DOI 10.1090/S0002-9947-1960-0120628-5
- Urs Lang, Quasi-minimizing surfaces in hyperbolic space, Math. Z. 210 (1992), no. 4, 581–592. MR 1175723, DOI 10.1007/BF02571815
- Urs Lang, The existence of complete minimizing hypersurfaces in hyperbolic manifolds, Internat. J. Math. 6 (1995), no. 1, 45–58. MR 1307303, DOI 10.1142/S0129167X95000055
- William Meeks III, Leon Simon, and Shing Tung Yau, Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature, Ann. of Math. (2) 116 (1982), no. 3, 621–659. MR 678484, DOI 10.2307/2007026
- Robert Meyerhoff, A lower bound for the volume of hyperbolic $3$-manifolds, Canad. J. Math. 39 (1987), no. 5, 1038–1056. MR 918586, DOI 10.4153/CJM-1987-053-6
- G. D. Mostow, Quasi-conformal mappings in $n$-space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math. 34 (1968), 53–104. MR 236383, DOI 10.1007/BF02684590
- Morgan Ward, Ring homomorphisms which are also lattice homomorphisms, Amer. J. Math. 61 (1939), 783–787. MR 10, DOI 10.2307/2371336
- James Munkres, Obstructions to the smoothing of piecewise-differentiable homeomorphisms, Ann. of Math. (2) 72 (1960), 521–554. MR 121804, DOI 10.2307/1970228
- M. H. A. Neumann, Quart. J. Math. 2 (1931), 1–8.
- Richard Schoen, Estimates for stable minimal surfaces in three-dimensional manifolds, Seminar on minimal submanifolds, Ann. of Math. Stud., vol. 103, Princeton Univ. Press, Princeton, NJ, 1983, pp. 111–126. MR 795231
- William P. Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 3, 357–381. MR 648524, DOI 10.1090/S0273-0979-1982-15003-0
- Friedhelm Waldhausen, On irreducible $3$-manifolds which are sufficiently large, Ann. of Math. (2) 87 (1968), 56–88. MR 224099, DOI 10.2307/1970594
- J. Weeks, SnapPea, undistributed version.
Bibliographic Information
- David Gabai
- Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
- MR Author ID: 195365
- Email: Gabai@cco.caltech.edu
- Received by editor(s): October 1, 1993
- Received by editor(s) in revised form: September 1, 1995
- Additional Notes: Partially supported by NSF Grants DMS-8902343, DMS-9200584, DMS-9505253 and SERC grant GR/H60851.
- © Copyright 1997 American Mathematical Society
- Journal: J. Amer. Math. Soc. 10 (1997), 37-74
- MSC (1991): Primary 57M50
- DOI: https://doi.org/10.1090/S0894-0347-97-00206-3
- MathSciNet review: 1354958