Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Finite dimensional Teichmüller spaces and generalizations

Author(s): Lipman Bers
Journal: Bull. Amer. Math. Soc. 5 (1981), 131-172.
MSC (1980): Primary 14H15, 30C60, 30F40, 32G15
MathSciNet review: 621883
Retrieve article in: PDF

References | Similar articles | Additional information

References:

1.
W. Abikoff, Some remarks on Kleinian groups, Advances in the Theory of Riemann Surfaces, Ann. of Math. Studies, No. 66, Princeton Univ. Press, Princeton, N. J., 1971, pp. 1-5. MR 288261
2.
W. Abikoff, On boundaries of Teichmüller spaces and on Kleinian groups. III, Acta Math. 134 (1975), 212-237. MR 435452
3.
W. Abikoff, Augmented Teichmüller spaces, Bull. Amer. Math. Soc. 82 (1976), 333-334. MR 432919
4.
W. Abikoff, Degenerating families of Riemann surfaces, Ann. of Math. (2) 105 (1977), 29-44. MR 442293
5.
W. Abikoff, Topics in the real analytic theory of Teichmüller space, Lecture Notes in Math., vol. 820, Springer-Verlag, Berlin and New York, 1980. MR 590044
6.
L. V. Ahlfors, On quasiconformal mappings, J. d'Analyse Math. 3 (1953/54), 1-58. MR 64875
7.
L. V. Ahlfors, The complex analytic structure of the space of closed Riemann surfaces, R. Nevanlinna et al., Analytic Functions, Princeton Univ. Press, Princeton, N. J., 1960, pp. 45-66. MR 124486
8.
L. V. Ahlfors, Curvature properties of Teichmüller's space, J. d'Analyse Math. 9 (1961), 161-176. MR 136730
9.
L. V. Ahlfors, Some remarks on Teichmüller's space of Riemann surfaces, Ann. of Math. (2) 74 (1961), 171-191. MR 204641
10.
L. V. Ahlfors, Quasiconformal reflections, Acta Math. 109 (1963), 291-301. MR 154978
11.
L. V. Ahlfors, Finitely generated Kleinian groups, Amer. J. Math. 86 (1964), 413-423; 87 (1965), 759. MR 167618
12.
L. V. Ahlfors, Fundamental polyhedrons and limit sets of Kleinian groups, Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 251-254. MR 194970
13.
L. V. Ahlfors, Lectures on quasiconformal mappings, Van Nostrand, New York, 1966. MR 200442
14.
L. V. Ahlfors, Quasiconformal mappings, Teichmüller spaces, and Kleinian groups, Proc. Internat. Congr. Math. (Helsinki 1978), pp. 71-84. MR 562598
15.
L. V. Ahlfors and L. Bers, Riemann's mapping theorem for variable metrics, Ann. of Math. (2) 72 (1960), 385-404. MR 115006
16.
W. L. Baily, Jr., On the theory of θ-functions, the moduli of abelian varieties, and the moduli of curves, Ann. of Math. (2) 75 (1962), 342-381. MR 162799
17.
L. Bers, Quasiconformal mappings and Teichmüller's theorem, R. Nevanlinna et. al., Analytic Functions, Princeton Univ. Press, Princeton, N. J., 1960, pp. 89-119. MR 114898
18.
L. Bers, Simultaneous uniformization, Bull. Amer. Math. Soc. 66 (1960), 94-97. MR 111834
19.
L. Bers, Correction to Spaces of Riemann surfaces as bounded domains, Bull. Amer. Math. Soc. 67 (1961), 465-466. MR 130972
20.
L. Bers, Uniformization by Beltrami equations, Comm. Pure. Appl. Math. 14 (1961), 215-228. MR 132175
21.
L. Bers, On moduli of Riemann surfaces, Lecture notes, E.T.H., Zurich, 1964.
22.
L. Bers, Automorphic forms and general Teichmüller spaces, Proc. Conf. Complex Analysis (Minneapolis, 1964) pp. 109-113, Springer-Verlag, Berlin and New York, 1965. MR 178142
23.
L. Bers, Automorphic forms and Poincaré series for infinitely generated Fuchsian groups, Amer. J. Math. 87 (1965), 196-214. MR 174737
24.
L. Bers, A non-standard integral equation with applications to quasiconformal mappings, Acta Math. 116 (1966), 113-134. MR 192046
25.
L. Bers, On boundaries of Teichmüller spaces and on Kleinian groups. I, Ann. of Math. (2) 91 (1970), 570-600. MR 297992
26.
L. Bers, Uniformization, moduli and Kleinian groups, Bull. London Math. Soc. 4 (1972), 257-300. MR 348097
27.
L. Bers, Fiber spaces over Teichmüller spaces, Acta Math. 130 (1973), 89-126. MR 430318
28.
L. Bers, On spaces of Riemann surfaces with nodes, Bull. Amer. Math. Soc. 80 (1974), 1219-1222. MR 361165
29.
L. Bers, Deformations and moduli of Riemann surfaces with nodes and signatures, Math. Scand. 36 (1975), 12-16. MR 374496
30.
L. Bers, Quasiconformal mappings, with applications to differential equations, function theory and topology, Bull. Amer. Math. Soc. 83 (1977), 1083-1100. MR 463433
31.
L. Bers, An extremal problem for quasiconformal mappings and a theorem by Thurston, Acta Math. 141 (1978), 73-98. MR 477161
32.
L. Bers, The action of the modular group on the complex boundary, Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference, Ann. of Math. Studies, No. 97 1981, pp. 33-52. MR 624803
33.
L. Bers and L. Ehrenpreis, Holomorphic convexity of Teichmüller spaces, Bull. Amer. Math. Soc. 70 (1964), 761-764. MR 168800
34.
L. Bers and L. Greenberg, Isomorphisms between Teichmüller spaces, Advances in the theory of Riemann surfaces, Ann. of Math. Studies, No. 66, 1971, pp. 53-79. MR 289763
35.
L. Bers and I. Kra, (eds.), A crash course on Kleinian groups, Lecture Notes in Math., vol. 400, Springer-Verlag, Berlin and New York, 1974. MR 346152
36.
A. Beurling and L. V. Ahlfors, The boundary correspondence under quasiconformal mappings, Acta Math. 96 (1956), 125-142. MR 86869
37.
R. Bowen, Hausdorff dimension of quasicircles, Inst. Hautes Études Sci. Publ. Math. 50 (1979), 153-170. MR 556580
38.
P. Buser, Riemannsche Flächen und Längenspektrum vom trigonometrischen Standpunkt aus Habilitationsschrift, Universität Bonn, 1980.
39.
T. Chu, The Weil-Petersson metric in the moduli space, Chinese J. Math. 4 (1976), 29-51. MR 590105
40.
P. Deligne and D. Mumford, The irreducibility of the space of curves of a given genus, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 75-109. MR 262240
41.
C. J. Earle, The Teichmüller space of an arbitrary Fuchsian group, Bull. Amer. Math. Soc. 70 (1964), 699-701. MR 172992
42.
C. J. Earle, Teichmüller spaces of groups of the second kind, Acta Math. 112 (1964), 91-97. MR 165096
43.
C. J. Earle, Reduced Teichmüller spaces, Trans. Amer. Math. Soc. 126 (1967), 54-63. MR 204642
44.
C. J. Earle, On holomorphic families of pointed Riemann surfaces, Bull. Amer. Math. Soc. 79 (1973), 163-166. MR 311898
45.
C. J. Earle, On the Carathéodory metric in Teichmüller spaces, Discontinuous Groups and Riemann Surfaces, Ann. of Math. Studies, No. 79, Princeton Univ. Press, Princeton, N. J., 1974, pp. 99-103. MR 352450
46.
C. J. Earle, The Teichmüller distance is differentiable, Duke Math. J. 44 (1977), 389-397. MR 445013
47.
C. J. Earle, Families of Riemann surfaces and their Jacobi varieties, Ann. of Math. 107 (1978), 255-286. MR 499328
48.
C. J. Earle and J. Eells, On the differential geometry of Teichmüller spaces, J. Analyse Math. 19 (1967), 35-52. MR 220923
49.
C. J. Earle and J. Eells, A fibre bundle description of Teichmüller theory, J. Differential Geom. 3 (1969), 19-43. MR 276999
50.
C. J. Earle and I. Kra, On holomorphic mappings between Teichmüller spaces, Contributions to Analysis, Academic Press, New York, 1974, pp. 107-124. MR 430319
51.
C. J. Earle and I. Kra, On sections of some holomorphic families of closed Riemann surfaces, Acta Math. 137 (1976), 49-79. MR 425183
52.
C. J. Earle and A. Marden (to appear).
53.
M. Engber, Teichmüller spaces and representability of functors, Trans. Amer. Math. Soc. 201 (1975), 213-226. MR 414939
54.
A. Fathi, F. Laudenbach and V. Poénaru, Travaux de Thurston sur les surfaces, Astérisque 66-67 (1979), 1-284. MR 568308
55.
L. Ford, Automorphic functions (second ed.), Chelsea, New York, 1951.
56.
R. Fricke and F. Klein, Vorlesungen über die Theorie der automorphen Funktionen (two volumes), B. G. Teubner, 1889 and 1926.
57.
F. P. Gardiner, On relative Teichmüller spaces and a globalization principle in Riemann surface theory, J. d'Analyse Math. 35 (1979), 1-12. MR 555298
58.
F. W. Gehring, Univalent functions and the Schwarzian derivative, Comment. Math. Helv. 52 (1977), 561-572. MR 457701
59.
F. W. Gehring, Spirals and the universal Teichmüller space, Acta Math. 141 (1978), 99-113. MR 499134
60.
J. Gilman, On the Nielsen type and the classification for the mapping-class group, Advances in Math. 40 (1981), 68-96. MR 616161
61.
L. Greenberg, Fundamental polyhedra for Kleinian groups, Ann. of Math. 84 (1966), 433-441. MR 200446
62.
A. Grothendieck, Techniques de construction en géometrie analytique, Sém. Cartan (1961/62) exp. 17, (with an appendix by J. P. Serre).
63.
K. T. Hahn, On the completeness of the Bergman metric and its subordinate metrics, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), 42-44. MR 417459
64.
N. Halpern, Some contributions to the theory of Riemann surfaces, Thesis, Columbia University, 1978.
65.
R. S. Hamilton, Extremal quasiconformal mappings with prescribed boundary values, Trans. Amer. Math. Soc. 138 (1969), 399-406. MR 245787
66.
W. J. Harvey, (ed.), Discrete groups and automorphic functions, Academic Press, New York, 1977. MR 498974
67.
J. H. Hubbard, Sur les sections analytique de la courbe universelle de Teichmüller, Mem. Amer. Math. Soc. No. 166, 1976, pp. 1-137. MR 430321
68.
J. Hubbard and H. Masur, Quadratic differentials and foliations, Acta Math. 142 (1979), 221-274. MR 523212
69.
J. A. Jenkins, On the existence of certain general extremal metrics, Ann. of Math. 66 (1957), 440-453. MR 90648
70.
L. Keen, On Fricke moduli. Advances in the Theory of Riemann Surfaces, Ann. of Math. Studies, No. 66, 1971, pp. 205-224. MR 288252
71.
S. P. Kerckhoff, The asymptotic geometry of Teichmüller space, Topology 19 (1980), 23-41. MR 559474
72.
S. Kobayashi, Hyperbolic manifolds and holomorphic mappings, M. Dekker, New York, 1970. MR 277770
73.
I. Kra, Automorphic forms and Kleinian groups, Benjamin, New York, 1972. MR 357775
74.
I. Kra, On new kinds of Teichmüller spaces, Israel J. Math. 16 (1973), 237-257. MR 364632
75.
I. Kra, On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces, Acta Math. 146 (1981), 231-270. MR 611385
76.
I. Kra and B. Maskit, Involutions on Kleinian groups, Bull. Amer. Math. Soc. 78 (1972), 801-805. MR 301190
77.
W. Kraus, Über den Zusammenhang einiger Charakteristiken eines eintach zusammehangenden Bereiches mit der Kreisabbildung, Mitt. Math. Sem. Giessen 21 (1932), 1-28.
78.
S. Kravetz, On the geometry of Teichmüller spaces and the structure of their modular groups, Ann. Acad. Sci. Fenn. 278 (1959), 1-35. MR 148906
79.
S. L. Krushkal, On Teichmüller's theorem on extremal quasiconformal mappings, Mat. Sb. 8 (1967), 313-332. (in Russian) MR 214761
80.
S. L. Krushkal, Quasiconformal mappings and Riemann surfaces, V. H. Winston and Sons, 1979. MR 536488
81.
O. Lehto and K. I. Virtanan, Quasiconformal mappings in the plane, Springer-Verlag, Berlin, 1973. MR 344463
82.
A. Marden, On homotopic mappings of Riemann surfaces, Ann. of Math. 90 (1969), 1-8. MR 249606
83.
B. Maskit, On Klein's combination theorem. II, Trans. Amer. Math. Soc. 131 (1968), 32-39. MR 223570
84.
B. Maskit, On boundaries of Teichmüller spaces and on Kleinian groups. II, Ann. of Math. 91 (1970), 607-639. MR 297993
85.
B. Maskit, On Klein's combination theorem. III, Advances in the Theory of Riemann Surfaces, Ann. of Math. Studies, No. 66, 1971, pp. 297-316. MR 289768
86.
B. Maskit, Moduli of marked Riemann surfaces, Bull. Amer. Math. Soc. 80 (1974), 773-777. MR 346149
87.
B. Maskit, On the classification of Kleinian groups. I. Koebe groups, Acta. Math. 135 (1975), 249-270. MR 444942
88.
B. Maskit, On the classification of Kleinian groups. II. Signatures, Acta. Math. 138 (1977), 17-42. MR 444943
89.
H. Masur, On a class of geodesics in Teichmüller space, Ann. of Math. 102 (1975), 205-221. MR 385173
90.
H. Masur, The extension of the Weil-Petersson metric to the boundary of Teichmüller spaces, Duke Math. J. 43 (1976), 623-635. MR 417456
91.
H. Masur, The Jenkins-Strebel differentials with one cylinder are dense, Comment. Math. Helv. 54 (1979), 179-184. MR 535053
92.
J. P. Matelski, A compactness theorem for Fuchsian groups of the second kind, Duke Math. J. 43 (1976), 829-840. MR 432921
93.
R. T. Miller, Nielsen's view point on geodesic laminations, Advances in Math. (to appear).
94.
D. Mumford, The structure of the moduli spaces of curves and abelian varieties, Proc. Intern. Congr. Math. (Nice 1970), vol. 1, pp. 457-465. MR 441983
95.
D. Mumford, Curves and their Jacobians, Univ. of Michigan Press, 1975. MR 419430
96.
Z. Nehari, Schwarzian derivatives and schlicht functions, Bull. Amer. Math. Soc. 55 (1949), 545-551. MR 29999
97.
B. O'Byrne, On Finsler geometry and applications to Teichmüller spaces, Advances in the Theory of Riemann surfaces, Ann. of Math. Studies, No. 66, 1971, pp. 317-328. MR 286141
98.
D. B. Patterson, The Teichmüller spaces are distinct, Proc. Amer. Math. Soc. 35 (1972), 179-182; 38 (1973), 668. MR 299774
99.
R. M. Porter, Computation of a boundary point of Teichmüller space, Bol. Soc. Mat. Mexicana 24 (1979), 15-26. MR 579666
100.
H. E. Rauch, On the transcendental moduli of algebraic Riemann surfaces, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 42-49. MR 72232
101.
H. E. Rauch, A transcendental view of the space of algebraic Riemann surfaces. Bull. Amer. Math. Soc. 71 (1965), 1-39. MR 213543
102.
E. Reich and K. Strebel, Extremal quasiconformal mappings with given boundary values, Bull. Amer. Math. Soc. 79 (1973), 488-490. MR 338362
103.
E. Reich and K. Strebel, Extremal quasiconformal mappings with given boundary values, Contributions to Analysis, Academic Press, New York, 1974, pp. 375-391. MR 361065
104.
H. L. Royden, Report on the Teichmüller metric, Proc. Nat. Acad. Sci. U.S.A. 65 (1970), 497-499. MR 259115
105.
H. L. Royden, Automorphisms and isometries of Teichmüller space, Advances in the Theory of Rieman Surfaces, Ann. of Math. Studies, No. 66, 1971, pp. 369-383. MR 288254
106.
M. Schiffer, A variational method for univalent quasi-conformal mappings, Duke Math. J. 33 (1966), 395-411. MR 197720
107.
K. Strebel, Zur Frage der Eindeutigkeit extremaler quasikonformer Abbildungen des Einheitskreises, Comment. Math. Helv. 36 (1961-62), 306-343; 39 (1964), 77-89. MR 176071
108.
K. Strebel, Über quadratische Differentiale mit geschlossenen Trajektorien und extremale quasikonforme Abbildungen, Festband zum 70 Geburtstag von Rolf Nevanlinna, Springer, Berlin, 1966, pp. 105-127. MR 209470
109.
K. Strebel, On quadratic differential and extremal quasiconformal mappings, Proc. Int. Cong. Math. (Vancouver, 1974), pp. 223-227. MR 507848
110.
K. Strebel, On quadratic differentials with closed trajectories on open Riemann surfaces, Ann. Acad. Sci. Fennicae 2 (1976), 533-551. MR 480991
111.
K. Strebel, On lifts of extremal quasiconformal mappings, J. d'Analyse Math. 31 (1977), 191-203. MR 585316
112.
K. Strebel, On quasiconformal mappings of open Riemann surfaces, Comment. Math. Helv. 53 (1978), 301-321. MR 505549
113.
D. Sullivan, On the ergodic theory of infinity of an arbitrary discrete group of hyperbolic motions, Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference, Ann. of Math. Studies, No. 97, 1980, pp. 465-496. MR 624833
114.
O. Teichmüller, Extremale quasikonforme Abbildungen und quadratische Differentiale, Preuss. Akad. 22 (1939).
115.
O. Teichmüller, Bestimmung der extremalen quasi konformen Abbildungen bei geschlossenen orientierten Riemannschen Flächen, Preuss Akad. 4 (1943). MR 17803
116.
O. Teichmüller, Veranderliche Riemannsche Flächen Deutsche Mathematik 7 (1949), 344-359. MR 18762
117.
W. P. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces. I, preprint. MR 956596
118.
W. P. Thurston, The geometry and topology of three-manifolds, Lecture Notes, Princeton University.
119.
P. Tukia, Quasiconformal extensions of quasisymmetric mappings compatible with a Fuchsian group (to appear).
120.
A. Weil, Sur les modules des surfaces de Riemann, Sém. Bourbaki, 1958. MR 124485
121.
S. Wolpert, Noncompleteness of the Weil-Petersson metric for Teichmüller space, Pacific J. Math. 61 (1975), 573-577. MR 422692

Similar Articles:

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1980): 14H15, 30C60, 30F40, 32G15

Retrieve articles in all Journals with MSC (1980): 14H15, 30C60, 30F40, 32G15


Additional Information:

DOI: 10.1090/S0273-0979-1981-14933-8
PII: S 0273-0979(1981)14933-8




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia