Available in electronic format
Available in print format
Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN: 1088-6834(e) ISSN: 0894-0347(p)
     

On the geometric and topological rigidity of hyperbolic 3-manifolds

Author(s): David Gabai
Journal: J. Amer. Math. Soc. 10 (1997), 37-74.
MSC (1991): Primary 57M50
Retrieve article in: PDF DVI PostScript
This article is available free of charge

References | Similar articles | Additional information

References:

[A]
M. Anderson, Complete Minimal Varieties in Hyperbolic Space, Invent. Math. 69 (1982), 477-494. MR 84c:53005

[BS]
F. Bonahon and L. Siebenmann, to appear.

[EM]
D. B. A. Epstein and A. Marden, Convex Hulls in Hyperbolic Space, a Theorem of Sullivan and Measured Pleated Surfaces, LMS Lect. Notes 111 (1984), 113-255. MR 89c:52014

[F]
W. Fenchel, Elementary Geometry in Hyperbolic Space, de Gruyter Stud. in Math. 11 (1989). MR 91a:51009

[FH]
M. H. Freedman and He, personal communication.

[FJ]
F. T. Farrell and L. Jones, A Topological analogue of Mostow's Rigidity Theorem, J. Amer. Math. Soc. 2 (1989), 257-370. MR 90h:57023a

[G1]
D. Gabai, Foliations and the Topology of 3-manifolds, J. Diff. Geom. 18 (1983), 445-503. MR 86a:57009

[G2]
-, Foliations and 3-manifolds, Proc. ICM Kyoto-1990 1 (1991), 609-619. MR 93d:57013

[G3]
-, Homotopy Hyperbolic 3-manifolds are Virtually Hyperbolic, JAMS 7 (1994), 193-198. MR 94b:57016

[GO]
D. Gabai and U. Oertel, Essential Laminations in 3-manifolds, Ann. of Math. (2) 130 (1989), 41-73. MR 90h:57012

[Gr]
M. Gromov, Hyperbolic Manifolds According to Thurston and Jorgensen, Sem. Bourbaki 32 (1979), 40-52. MR 84b:53046

[GS]
R. Gulliver and P. Scott, Least Area Surfaces Can Have Excess Triple Points, Topology 26 (1987), 345-359. MR 88k:57018

[HS]
J. Hass and P. Scott, The Existence of Least Area Surfaces in 3-manifolds, Trans. AMS 310 (1988), 87-114. MR 90c:53022

[Ki]
J. M. Kister, Isotopies in 3-manifolds, Trans. AMS 97 (1960), 213-224. MR 22:11378

[L1]
U. Lang, Quasi-minimizing Surfaces in Hyperbolic Space, Math. Zeit. 210 (1992), 581-592. MR 93e:53008

[L2]
-, The Existence of Complete Minimizing Hypersurfaces in Hyperbolic Manifolds, Int. J. Math. 6 (1995), 45-58. MR 95i:58053

[MSY]
W. H. Meeks III, L. Simon, S. T. Yau, Embedded Minimal Surfaces, Exotic Spheres, and Manifolds with Positive Ricci Curvature, Ann. of Math (2) 91 (1982), 621-659. MR 84f:53053

[Me]
R. Meyerhoff, A Lower Bound for the Volume of Hyperbolic 3-manifolds, Can. J. Math. 39 (1987), 1038-1056. MR 88k:57049

[Mo]
G. D. Mostow, Quasiconformal Mappings in n-Space and the Rigidity of Hyperbolic Space Forms, Pub. IHES 34 (1968), 53-104. MR 38:4679

[Mor]
C. B. Morrey, The Problem of Plateau in a Riemannian Manifold, Ann. Math (2) 49 (1948), 807-851. MR 10:259f

[Mu]
J. R. Munkres, Obstructions to Smoothing Piecewise Differentiable Homeomorphisms, Ann. Math (2) 72 (1960), 521-554. MR 22:12534

[Ne]
M. H. A. Neumann, Quart. J. Math. 2 (1931), 1-8.

[S]
R. Schoen, Estimates for Stable Minimal Surfaces in Three Dimensional Manifolds, Ann. of Math. Stud. 103 (1983), 111-126. MR 86j:53094

[Th]
William P. Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 3, 357-381. MR 83h:57019

[W]
F. Waldhausen, On Irreducible 3-manifolds which are Sufficiently Large, Annals of Math. 87 (1968), 56-88. MR 36:7146

[We]
J. Weeks, SnapPea, undistributed version.


Similar Articles:

Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 57M50

Retrieve articles in all Journals with MSC (1991): 57M50


Additional Information:

David Gabai
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: Gabai@cco.caltech.edu

DOI: 10.1090/S0894-0347-97-00206-3
PII: S 0894-0347(97)00206-3
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 of article: Copyright 1997, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google