Quasirigidity of hyperbolic $3$-manifolds and scattering theory
David Borthwick, Alan McRae, and Edward C. Taylor
Source: Duke Math. J. Volume 89, Number 2
(1997), 225-236.
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/1077241017
Mathematical Reviews number (MathSciNet): MR1460622
Zentralblatt MATH identifier: 0915.30037
Digital Object Identifier: doi:10.1215/S0012-7094-97-08912-2
References
[1] L. 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. Ahlfors, Fundamental polyhedrons and limit point sets of Kleinian groups, Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 251–254.
Mathematical Reviews (MathSciNet): MR33:3175
Zentralblatt MATH: 0132.30801
Digital Object Identifier: doi:10.1073/pnas.55.2.251
JSTOR: links.jstor.org
[3] L. Ahlfors and L. Bers, Riemann's mapping theorem for variable metrics, Ann. of Math. (2) 72 (1960), 385–404.
Mathematical Reviews (MathSciNet): MR22:5813
Zentralblatt MATH: 0104.29902
Digital Object Identifier: doi:10.2307/1970141
JSTOR: links.jstor.org
[4] K. Astala, Area distortion of quasiconformal mappings, Acta Math. 173 (1994), no. 1, 37–60.
Mathematical Reviews (MathSciNet): MR95m:30028b
Zentralblatt MATH: 0815.30015
Digital Object Identifier: doi:10.1007/BF02392568
[5] L. Bers, On moduli of Kleinian groups, Russian Math. Surveys 29 (1974), 88–102.
Zentralblatt MATH: 0304.30013
Mathematical Reviews (MathSciNet): MR422691
[6] D. Borthwick and E. C. Taylor, Quasi-rigidity of hyperbolic $3$-manifolds and scattering theory, II, in preparation.
[7] R. Canary and E. C. Taylor, Kleinian groups with small limit sets, Duke Math. J. 73 (1994), no. 2, 371–381.
Mathematical Reviews (MathSciNet): MR94m:57028
Zentralblatt MATH: 0798.30030
Digital Object Identifier: doi:10.1215/S0012-7094-94-07316-X
Project Euclid: euclid.dmj/1077288815
[8] A. Douady and C. 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] F. W. Gehring and J. Väisälä, Hausdorff dimension and quasiconformal mappings, J. London Math. Soc. (2) 6 (1973), 504–512.
Mathematical Reviews (MathSciNet): MR48:2380
Zentralblatt MATH: 0258.30020
Digital Object Identifier: doi:10.1112/jlms/s2-6.3.504
[10] N. Mandouvalos, Scattering operator, Eisenstein series, inner product formula and “Maass-Selberg” relations for Kleinian groups, Mem. Amer. Math. Soc. 78 (1989), no. 400, iv+87.
Mathematical Reviews (MathSciNet): MR90c:11036
Zentralblatt MATH: 0673.10023
[11] 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
[12] 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
[13] R. Mazzeo and R. Melrose, Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature, J. Funct. Anal. 75 (1987), no. 2, 260–310.
Mathematical Reviews (MathSciNet): MR89c:58133
Zentralblatt MATH: 0636.58034
Digital Object Identifier: doi:10.1016/0022-1236(87)90097-8
[14] R. Melrose, Geometric scattering theory, Stanford Lectures, Cambridge University Press, Cambridge, 1995.
Mathematical Reviews (MathSciNet): MR96k:35129
Zentralblatt MATH: 0849.58071
[15] P. Nicholls, The Ergodic Theory of Discrete Groups, London Mathematical Society Lecture Note Series, vol. 143, Cambridge University Press, Cambridge, 1989.
Mathematical Reviews (MathSciNet): MR91i:58104
Zentralblatt MATH: 0674.58001
[16] P. Perry, The Laplace operator on a hyperbolic manifold. II. Eisenstein series and the scattering matrix, J. Reine Angew. Math. 398 (1989), 67–91.
Mathematical Reviews (MathSciNet): MR90g:58138
Zentralblatt MATH: 0677.58044
Digital Object Identifier: doi:10.1515/crll.1989.398.67
[17] P. Perry, A trace-class rigidity theorem for Kleinian groups, Ann. Acad. Sci. Fenn. Ser. A I Math. 20 (1995), no. 2, 251–257.
Mathematical Reviews (MathSciNet): MR96i:58175
Zentralblatt MATH: 0861.57017
[18] H. M. Reimann, Invariant extension of quasiconformal deformations, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 477–492.
Mathematical Reviews (MathSciNet): MR87a:30038
Zentralblatt MATH: 0592.30025
[19] W. Thurston, The geometry and topology of $3$-manifolds, lecture notes, Princeton University, 1979.
[20] J. Väisälä, Lectures on $n$-dimensional quasiconformal mappings, Springer-Verlag, Berlin, 1971.
Mathematical Reviews (MathSciNet): MR56:12260
Duke Mathematical Journal