Riemann surfaces and the geometrization of 3-manifolds

McMullen, Curt

doi:10.1090/S0273-0979-1992-00313-0

Riemann surfaces and the geometrization of 3-manifolds
HTML articles powered by AMS MathViewer

by Curt McMullen PDF

Bull. Amer. Math. Soc. 27 (1992), 207-216 Request permission

References

David E. Barrett and Jeffrey Diller, Poincaré series and holomorphic averaging, Invent. Math. 110 (1992), no. 1, 23–27. MR 1181813, DOI 10.1007/BF01231321
Lipman Bers, Simultaneous uniformization, Bull. Amer. Math. Soc. 66 (1960), 94–97. MR 111834, DOI 10.1090/S0002-9904-1960-10413-2
Lipman Bers, Uniformization, moduli, and Kleinian groups, Bull. London Math. Soc. 4 (1972), 257–300. MR 348097, DOI 10.1112/blms/4.3.257
Lipman Bers, An extremal problem for quasiconformal mappings and a theorem by Thurston, Acta Math. 141 (1978), no. 1-2, 73–98. MR 477161, DOI 10.1007/BF02545743
Lipman Bers, Finite-dimensional Teichmüller spaces and generalizations, Bull. Amer. Math. Soc. (N.S.) 5 (1981), no. 2, 131–172. MR 621883, DOI 10.1090/S0273-0979-1981-14933-8
Robert Brooks, The fundamental group and the spectrum of the Laplacian, Comment. Math. Helv. 56 (1981), no. 4, 581–598. MR 656213, DOI 10.1007/BF02566228
Adrien Douady and John H. Hubbard, A proof of Thurston’s topological characterization of rational functions, Acta Math. 171 (1993), no. 2, 263–297. MR 1251582, DOI 10.1007/BF02392534
Travaux de Thurston sur les surfaces, Astérisque, vol. 66, Société Mathématique de France, Paris, 1979 (French). Séminaire Orsay; With an English summary. MR 568308
Frederick P. Gardiner, Teichmüller theory and quadratic differentials, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1987. A Wiley-Interscience Publication. MR 903027
Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549
Mikhael Gromov, Structures métriques pour les variétés riemanniennes, Textes Mathématiques [Mathematical Texts], vol. 1, CEDIC, Paris, 1981 (French). Edited by J. Lafontaine and P. Pansu. MR 682063
Terry Lyons and Dennis Sullivan, Function theory, random paths and covering spaces, J. Differential Geom. 19 (1984), no. 2, 299–323. MR 755228
Curt McMullen, Amenability, Poincaré series and quasiconformal maps, Invent. Math. 97 (1989), no. 1, 95–127. MR 999314, DOI 10.1007/BF01850656
C. McMullen, Iteration on Teichmüller space, Invent. Math. 99 (1990), no. 2, 425–454. MR 1031909, DOI 10.1007/BF01234427
Curt McMullen, Rational maps and Kleinian groups, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990) Math. Soc. Japan, Tokyo, 1991, pp. 889–899. MR 1159274
Curt McMullen, Amenable coverings of complex manifolds and holomorphic probability measures, Invent. Math. 110 (1992), no. 1, 29–37. MR 1181814, DOI 10.1007/BF01231322
John W. Morgan, On Thurston’s uniformization theorem for three-dimensional manifolds, The Smith conjecture (New York, 1979) Pure Appl. Math., vol. 112, Academic Press, Orlando, FL, 1984, pp. 37–125. MR 758464, DOI 10.1016/S0079-8169(08)61637-2

Strong rigidity of locally symmetric spaces

David Mumford, A remark on Mahler’s compactness theorem, Proc. Amer. Math. Soc. 28 (1971), 289–294. MR 276410, DOI 10.1090/S0002-9939-1971-0276410-4
Hiromi Ohtake, Lifts of extremal quasiconformal mappings of arbitrary Riemann surfaces, J. Math. Kyoto Univ. 22 (1982/83), no. 2, 191–200. MR 666970, DOI 10.1215/kjm/1250521809
Jean-Paul Pier, Amenable locally compact groups, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1984. A Wiley-Interscience Publication. MR 767264
H. Poincare, Mémoire sur les fonctions fuchsiennes, Acta Math. 1 (1882), no. 1, 193–294 (French). MR 1554584, DOI 10.1007/BF02391845
Kurt Strebel, On lifts of extremal quasiconformal mappings, J. Analyse Math. 31 (1977), 191–203. MR 585316, DOI 10.1007/BF02813303
Dennis 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. MR 624833
Dennis Sullivan, Quasiconformal homeomorphisms in dynamics, topology, and geometry, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 1216–1228. MR 934326
Dennis Sullivan, Bounds, quadratic differentials, and renormalization conjectures, American Mathematical Society centennial publications, Vol. II (Providence, RI, 1988) Amer. Math. Soc., Providence, RI, 1992, pp. 417–466. MR 1184622

Geometry and topology of three-manifolds

William P. Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 3, 357–381. MR 648524, DOI 10.1090/S0273-0979-1982-15003-0
William P. Thurston, Hyperbolic structures on $3$-manifolds. I. Deformation of acylindrical manifolds, Ann. of Math. (2) 124 (1986), no. 2, 203–246. MR 855294, DOI 10.2307/1971277
William P. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. (N.S.) 19 (1988), no. 2, 417–431. MR 956596, DOI 10.1090/S0273-0979-1988-15685-6

Hyperbolic structures on

manifolds

Surface groups and

manifolds which fiber over the circle

Hyperbolic structures on

manifolds

Deformation of

manifolds with incompressible boundary

Hyperbolic structures on

manifolds

Construction of hyperbolic manifolds

On the combinatorics and dynamics of iterated rational maps