Complex earthquakes and teichmüller theory

Journal of the American Mathematical Society

Volumn 11, Issue 2, 1998, Pages 283-320

  Mcmullen, Curtis T ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032385282     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0894-0347-98-00259-8     Document Type: Article

References (50)

1. J. Anderson and R. Canary. Algebraic limits of Kleinian groups which rearrange the pages of a book. Invent. math. 126(1996), 205-214. MR 97h:57025
2. L. Bers. Simultaneous uniformization. Bull. Amer. Math. Soc. 66(1960), 94-97. MR 22:2694
3. L. Bers. On boundaries of Teichmüller spaces and on kleinian groups: I. Annals of Math. 91(1970), 570-600. MR 45:7044
4. L. Bers. Holomorphic families of isomorphisms of Möbius groups. J. of Math. of Kyoto University 26(1986), 73-76. MR 87j:32067
5. L. Bers and L. Ehrenpreis. Holomorphic convexity of Teichmüller spaces. Bull. Amer. Math. Soc. 70(1964), 761-764. MR 29:6056
6. F. Bonahon, Bouts des variétés hyperboliques de dimension 3. Annals of Math. 124(1986), 71-158. MR 88c:57013
7. F. Bonahon. The geometry of Teichmüller space via geodesic currents. Invent. math. 92(1988), 139-162. MR 90a:32025
8. C. J. Earle. On variation of projective structures. In I. Kra and B. Maskit, editors, Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference, pages 87-99. Annals of Math. Studies 97. Princeton, 1981. MR 83a:32017
9. D. B. A. Epstein and A. Marden. Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces. In Analytical and Geometric Aspects of Hyperbolic Space, pages 113-254. Cambridge University Press, 1987. MR 89c:52014
10. G. Faltings. Real projective structures on Riemann surfaces. Comp. Math. 48(1983), 223-269. MR 85d:32046
11. A. Fathi, F. Laudenbach, and V. Poénaru. Travaux de Thurston sur les surfaces. Astérisque, volume 66-67, 1979.
12. F. Gardiner. Teichmüller Theory and Quadratic Differentials. Wiley Interscience, 1987. MR 88m:32044
13. W. M. Goldman. Projective structures with Fuchsian holonomy. J. Diff. Geom. 25(1987), 297-326. MR 88i:57006
14. J. J. Gray. Fuchs and the theory of differential equations. Bull. Amer. Math. Soc. 10(1984), 1-26. MR 85h:01020a; MR 85h:0102
15. R. Gunning. Lectures on Vector Bundles over Riemann Surfaces. Princeton University Press, 1967. MR 37:5888
16. R. C. Gunning. Affine and projective structures on Riemann surfaces. In I. Kra and B. Maskit, editors, Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference. Annals of Math. Studies 97, Princeton, 1981. MR 83g:30054
17. D. A. Hejhal. Monodromy groups and linearly polymorphic functions. Acta. Math. 135(1975), 1-55. MR 57:3380
18. C. Hodgson and S. Kerckhoff. Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery. Preprint, 1995.
19. J. H. Hubbard. The monodromy of projective structures. In I. Kra and B. Maskit, editors, Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference. Annals of Math. Studies 97, Princeton, 1981. MR 82k:14009
20. Y. Imayoshi and M. Taniguchi. An Introduction to Teichmüller Spaces. Springer-Verlag, 1992. MR 94b:32031
21. Y. Kamishima and Ser P. Tan. Deformation spaces on geometric structures. In Y. Matsunioto and S. Morita, editors, Aspects of Low Dimensional Manifolds, pages 263-300. Published for Math. Soc. of Japan by Kinokuniya Co., 1992. MR 94k:57023
22. L. Keen and C. Series. Pleating coordinates for the Maskit embedding of the Teichmüller space of a punctured torus. Topology 32(1993), 719-749. MR 95g:32030
23. S. Kerckhoff. The Nielsen realization problem. Ann. of Math. 177(1983), 235-265. MR 85e:32029
24. S. Kerckhoff. Earthquakes are analytic. Comment. Math. Helvetici 60(1985), 17-30. MR 86m:57014
25. S. Kerckhoff and W. Thurston. Non-continuity of the action of the modular group at Bers' boundary of Teichmüller space. Invent. math. 100(1990), 25-48. MR 91a:57038
26. I. Kra. Deformation spaces. In A Crash Course on Kleinian Groups, Lecture Notes in Math. 400, pages 48-70. Springer-Verlag, 1974. MR 53:5943
27. O. Lehto. Univalent functions and Teichmüller spaces. Springer-Verlag, 1987. MR 88f:30073
28. B. Maskit. On a class of Kleinian groups. Ann. Acad. Sci. Fenn. Ser. A 442(1969), 1-8. MR 40:5857
29. S. Matsumoto. Foundations of flat conformal structure. In Y. Matsumoto and S. Morita, editors, Aspects of Low Dimensional Manifolds, pages 167-262. Published for Math. Soc. of Japan by Kinokuniya Co., 1992. MR 93m:57014
30. C. McMullen. Iteration on Teichmüller space. Invent. math. 99(1990), 425-454. MR 91a:57008
31. C. McMullen. Renormalization and 3-Manifolds which Fiber over the Circle. Annals of Math Studies 142, Princeton University Press, 1996. MR 97f:57022
32. Y. Minsky. The classification of punctured torus groups. SUNY Preprint 1997/6.
33. D. Mumford, C. McMullen, and D. Wright. Limit sets of free two-generator kleinian groups. Preprint, 1990.
34. S. Nag. The Complex Analytic Theory of Teichmüller Space. Wiley, 1988. MR 89f:32040
35. J.-P. Otal. Le théorème d'hyperbolisation pour les variétés fibrées de dimension trois. Astérisque, volume 235, 1996. MR 97e:57013
36. J. R. Parker and C. Series. Bending formulae for convex hull boundaries. J. d'Analyse Math. 67(1995), 165-198. MR 97k:30057
37. H. Shiga. On analytic and geometric properties of Teichmüller spaces. J. Math. Kyoto Univ. 24(1984), 441-452. MR 86c:32024
38. H. Shiga and H. Tanigawa. Projective structures with discrete holonomy representations. Trans. Amer. Math. Soc., To appear. CMP 97:11
39. D. Sullivan. Quasiconformal homeomorphisms and dynamics II: Structural stability implies hyperbolicity for Kleinian groups. Acta Math. 155(1985), 243-260. MR 87i:58104
40. H. Tanigawa. Grafting, harmonic maps and projective structures on surfaces. Preprint, 1995.
41. W. P. Thurston. Geometry and Topology of Three-Manifolds. Lecture Notes, Princeton University, 1979.
42. W. P. Thurston. Earthquakes in two-dimensional hyperbolic geometry. In D. B. Epstein, editor, Low-dimensional Topology and Kleinian Groups. Cambridge Univ. Press, 1987. MR 88m:57015
43. W. P. Thurston. Three-Dimensional Geometry and Topology, volume 1. Princeton University Press, 1997. MR 97m:57016
44. W. P. Thurston. Hyperbolic structures on 3-manifolds II: Surface groups and 3-manifolds which fiber over the circle. Preprint.
45. M. Wolf. The Teichmüller theory of harmonic maps. J. Diff. Geom. 29(1989), 449-479. MR 90h:58023
46. S. Wolpert. An elementary formula for the Fenchel-Xielsen twist. Comment. Math. Helv. 56(1981), 132-135. MR 82k:32053
47. S. Wolpert. The Fenchel-Nielsen deformation. Annals of Math. 115(1982), 501-528. MR 83g:32024
48. S. Wolpert. On the Weil-Petersson geometry of the moduli space of curves. Amer. J. Math. 107(1985), 969-997. MR 87b:32040
49. S. Wolpert. Geodesic length functions and the Nielsen problem. J. Diff. Geom. 25(1987), 275-296. MR 88e:32032
50. D. Wright. The shape of the boundary of Maskit's embedding of the Teichmüller space of once-punctured tori. Preprint, 1990.