The Poincaré metric and a conformal version of a theorem of Thurston
Richard D. Canary
Source: Duke Math. J. Volume 64, Number 2
(1991), 349-359.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077295526
Mathematical Reviews number (MathSciNet): MR1136380
Zentralblatt MATH identifier: 0759.57013
Digital Object Identifier: doi:10.1215/S0012-7094-91-06417-3
References
[1] L. V. Ahlfors, Finitely generated Kleinian groups, Amer. J. Math. 86 (1964), 413–429.
Mathematical Reviews (MathSciNet): MR29:4890
Zentralblatt MATH: 0133.04201
Digital Object Identifier: doi:10.2307/2373173
JSTOR: links.jstor.org
[2] L. V. Ahlfors, Conformal invariants: topics in geometric function theory, McGraw-Hill Book Co., New York, 1973.
Mathematical Reviews (MathSciNet): MR50:10211
Zentralblatt MATH: 0272.30012
[3] A. F. Beardon and Ch. Pommerenke, The Poincaré metric of plane domains, J. London Math. Soc. (2) 18 (1978), no. 3, 475–483.
Mathematical Reviews (MathSciNet): MR80a:30020
Zentralblatt MATH: 0399.30008
Digital Object Identifier: doi:10.1112/jlms/s2-18.3.475
[4] L. Bers, On boundaries of Teichmüller spaces and on Kleinian groups. I, Ann. of Math. (2) 91 (1970), 570–600.
Mathematical Reviews (MathSciNet): MR45:7044
Zentralblatt MATH: 0197.06001
Digital Object Identifier: doi:10.2307/1970638
JSTOR: links.jstor.org
[5] L. Bers, Spaces of Kleinian groups, Several Complex Variables, I (Proc. Conf., Univ. of Maryland, College Park, Md., 1970), Lecture Notes in Math., vol. 155, Springer, Berlin, 1970, pp. 9–34.
Mathematical Reviews (MathSciNet): MR42:6216
Zentralblatt MATH: 0211.10602
[6] R. D. Canary, Hyperbolic structures on $3$-manifolds with compressible boundary, Ph.D. thesis, Princeton Univ., June 1989.
[7] R. D. Canary, Algebraic convergence of Schottky groups, preprint.
Mathematical Reviews (MathSciNet): MR1137257
Zentralblatt MATH: 0772.30037
Digital Object Identifier: doi:10.2307/2154320
JSTOR: links.jstor.org
[8] A. Douady and C. J. Earle, Conformally natural extension of homeomorphisms of the circle, Acta Math. 157 (1986), no. 1-2, 23–48.
Mathematical Reviews (MathSciNet): MR87j:30041
Zentralblatt MATH: 0615.30005
Digital Object Identifier: doi:10.1007/BF02392590
[9] 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.
Mathematical Reviews (MathSciNet): MR89c:52014
Zentralblatt MATH: 0612.57010
[10] I. Kra, On spaces of Kleinian groups, Comment. Math. Helv. 47 (1972), 53–69.
Mathematical Reviews (MathSciNet): MR46:5611
Zentralblatt MATH: 0239.30020
Digital Object Identifier: doi:10.1007/BF02566788
[11] I. Kra and B. Maskit, Remarks on projective structures, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978), Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 343–359.
Mathematical Reviews (MathSciNet): MR83f:30042
Zentralblatt MATH: 0486.30034
[12] A. Marden, The geometry of finitely generated kleinian groups, Ann. of Math. (2) 99 (1974), 383–462.
Mathematical Reviews (MathSciNet): MR50:2485
Zentralblatt MATH: 0282.30014
Digital Object Identifier: doi:10.2307/1971059
JSTOR: links.jstor.org
[13] B. Maskit, Self-maps on Kleinian groups, Amer. J. Math. 93 (1971), 840–856.
Mathematical Reviews (MathSciNet): MR45:544
Zentralblatt MATH: 0227.32007
Digital Object Identifier: doi:10.2307/2373474
JSTOR: links.jstor.org
[14] B. Maskit, Parabolic elements in Kleinian groups, Ann. of Math. (2) 117 (1983), no. 3, 659–668.
Mathematical Reviews (MathSciNet): MR85a:30073
Zentralblatt MATH: 0527.30038
Digital Object Identifier: doi:10.2307/2007038
JSTOR: links.jstor.org
[15] B. Maskit, Comparison of hyperbolic and extremal lengths, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 381–386.
Mathematical Reviews (MathSciNet): MR87c:30062
Zentralblatt MATH: 0587.30043
[16] B. Maskit, Kleinian groups, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 287, Springer-Verlag, Berlin, 1988.
Mathematical Reviews (MathSciNet): MR90a:30132
Zentralblatt MATH: 0627.30039
[17] C. McMullen, Cusps are dense, Ann. of Math. (2) 133 (1991), no. 1, 217–247.
Mathematical Reviews (MathSciNet): MR91m:30058
Zentralblatt MATH: 0718.30033
Digital Object Identifier: doi:10.2307/2944328
JSTOR: links.jstor.org
[18] J. W. Morgan and P. Shalen, Valuations, trees, and degenerations of hyperbolic structures. I, Ann. of Math. (2) 120 (1984), no. 3, 401–476.
Mathematical Reviews (MathSciNet): MR86f:57011
Zentralblatt MATH: 0583.57005
Digital Object Identifier: doi:10.2307/1971082
JSTOR: links.jstor.org
[19] J. W. Morgan and P. Shalen, Degenerations of hyperbolic structures. II. Measured laminations in $3$-manifolds, Ann. of Math. (2) 127 (1988), no. 2, 403–456.
Mathematical Reviews (MathSciNet): MR89e:57010a
Zentralblatt MATH: 0656.57003
Digital Object Identifier: doi:10.2307/2007061
JSTOR: links.jstor.org
[20] J. W. Morgan and P. Shalen, Degenerations of hyperbolic structures. III. Actions of $3$-manifold groups on trees and Thurston's compactness theorem, Ann. of Math. (2) 127 (1988), no. 3, 457–519.
Mathematical Reviews (MathSciNet): MR89e:57010b
Zentralblatt MATH: 0661.57004
Digital Object Identifier: doi:10.2307/2007003
JSTOR: links.jstor.org
[21] K. Ohshika, On limits of quasi-conformal deformations of Kleinian groups, Math. Z. 201 (1989), no. 2, 167–176.
Mathematical Reviews (MathSciNet): MR90f:30058
Zentralblatt MATH: 0681.30025
Digital Object Identifier: doi:10.1007/BF01160674
[22] B. Randol, Cylinders in Riemann surfaces, Comment. Math. Helv. 54 (1979), no. 1, 1–5.
Mathematical Reviews (MathSciNet): MR80j:30065
Zentralblatt MATH: 0401.30036
Digital Object Identifier: doi:10.1007/BF02566252
[23] A. Selberg, On discontinuous groups in higher-dimensional symmetric spaces, Contributions to function theory (internat. Colloq. Function Theory, Bombay, 1960), Tata Institute of Fundamental Research, Bombay, 1960, pp. 147–164.
Mathematical Reviews (MathSciNet): MR24:A188
Zentralblatt MATH: 0201.36603
[24] D. Sullivan, On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978), Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 465–496.
Mathematical Reviews (MathSciNet): MR83f:58052
Zentralblatt MATH: 0567.58015
[25] W. Thurston, Hyperbolic structures on $3$-manifolds. I. Deformation of acylindrical manifolds, Ann. of Math. (2) 124 (1986), no. 2, 203–246.
Mathematical Reviews (MathSciNet): MR88g:57014
Zentralblatt MATH: 0668.57015
Digital Object Identifier: doi:10.2307/1971277
JSTOR: links.jstor.org
[26] W. Thurston, Hyperbolic structures on $3$-manifolds, II: surface groups and $3$-manifolds which fiber over the circle, preprint.
[27] W. Thurston, Hyperbolic structures on $3$-manifolds, III: deformations of $3$-manifolds with incompressible boundary, preprint.
Duke Mathematical Journal