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