On the geometric and topological rigidity of hyperbolic 3-manifolds

Gabai, David

doi:10.1090/S0894-0347-97-00206-3

On the geometric and topological rigidity of hyperbolic 3-manifolds
HTML articles powered by AMS MathViewer

by David Gabai

J. Amer. Math. Soc. 10 (1997), 37-74

DOI: https://doi.org/10.1090/S0894-0347-97-00206-3

PDF | Request permission

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.