|
Riemann surfaces and the geometrization of 3-manifolds
Author(s):
Curt
McMullen
Journal:
Bull. Amer. Math. Soc.
27
(1992),
207-216.
MSC (2000):
Primary 57M99, 30C75
MathSciNet review:
1153266
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- [BD]
- {Barrett:Diller}D.~Barrett and J.~Diller, {\em Poincar\'e series and holomorphic averaging}, Invent. Math. (to appear). MR 1181813
- [Bers1]
- {Bers:simunif}L.~Bers, {\em Simultaneous uniformization},Bull. Amer. Math. Soc. {\bf 66} (1960), 94--97. MR 111834
- [Bers2]
- {Bers:London:survey}\bysame {\em Uniformization, moduli and Kleinian groups}, Bull. London Math. Soc. {\bf 4} (1972), 257--300. MR 348097
- [Bers3]
- {Bers:mcg}\bysame {\em An extremal problem for quasiconformal maps and a theorem by Thurston}, Acta Math. {\bf 141} (1978), 73--98. MR 477161
- [Bers4]
- {Bers:ts:survey}\bysame {\em Finite dimensional Teichm\"uller spaces and generalizations}, Bull. Amer. Math. Soc. {\bf 5} (1981), 131--172. MR 621883
- [Br]
- {Brooks:amenable}R.~Brooks, {\em The fundamental group and the spectrum of the Laplacian}, Comment. Math. Helv. {\bf 56} (1985), 581--596. MR 656213
- [DH]
- {Douady:Hubbard:Thurston}A.~Douady and J.~Hubbard, {\em A proof of Thurston's topological characterization of rational maps}, Acta Math. (to appear). MR
- [FLP]
- {FLP}A.~Fathi, F.~Laudenbach, and V.~Po\'enaru, {\em Travaux de Thurston sur les surfaces}, Asterisque, vol. 66-67, Soc. Math. France,Paris, 1979. MR 568308
- [Gard]
- {Gardiner:book}F.~Gardiner, {\em Teichm\"{u}ller theory and quadratic differentials}, Wiley Interscience, 1987. MR 903027
- [Gre]
- {Greenleaf:book}F.~P. Greenleaf, {\em Invariant means on topological groups}, Van Nostrand, 1969. MR 251549
- [Grom]
- {Gromov:book}M.~Gromov, {\em Structures m\'{e}triques pour les vari\'{e}t\'{e}s riemanniennes}, Textes Math., vol. 1, CEDIC, Paris, 1981. MR 682063
- [LS]
- {Lyons:Sullivan}T.~Lyons and D.~Sullivan, {\em Function theory, random paths and covering spaces}, J. Differential Geom. {\bf 19} (1984), 299--323. MR 755228
- [Mc1]
- {McMullen:amenable}C.~McMullen, {\em Amenability, Poincar\'{e} series and quasiconformal maps}, Invent. Math. {\bf 97} (1989), 95--127. MR 999314
- [Mc2]
- {McMullen:iter}\bysame {\em Iteration on Teichm\"uller space}, Invent. Math. {\bf 99} (1990), 425--454. MR 1031909
- [Mc3]
- {McMullen:icm90}\bysame {\em Rational maps and Kleinian groups},Proceedings of the International Congress of Mathematicians Kyoto 1990, Springer-Verlag, 1991, pp. 889--900. MR 1159274
- [Mc4]
- {McMullen:newamen}\bysame {\em Amenable coverings of complex manifolds and holomorphic probability measures}, Invent. Math. (to appear). MR 1181814
- [Mor]
- {Morgan:uniformization}J.~Morgan, {\em On Thurston's uniformization theorem for three dimensional manifolds}, The Smith Conjecture, Academic Press, 1984, pp. 37--125. MR 758464
- [Mos]
- {Mostow:book}D.~Mostow, {\em Strong rigidity of locally symmetric spaces}, Ann. of Math Stud., vol. 78, Princeton Univ. Press, Princeton, NJ, 1972. MR
- [Mum]
- {Mumford:compact}D.~Mumford, {\em A remark on Mahler's compactness theorem}, Proc. Amer. Math. Soc. {\bf 28} (1971), 289--294. MR 276410
- [Oh]
- {Ohtake:theta}H.~Ohtake, {\em Lifts of extremal quasiconformal mappings of arbitrary Riemann surfaces}, J. Math. Kyoto Univ. {\bf 22} (1982), 191--200. MR 666970
- [Pier]
- {Pier:book}J.~P. Pier, {\em Amenable locally compact groups}, Wiley Interscience, New York, 1984. MR 767264
- [Poin]
- {Poincare:fuchsian}H.~Poincar\'{e}, {\em M\'{e}moire sur les fonctions Fuchsiennes}, Acta Math. {\bf 1} (1882/3), 193--294. MR 1554584
- [Str]
- {Strebel:theta}K.~Strebel, {\em On lifts of extremal quasiconformal mappings}, J. d'Analyse Math. {\bf 31} (1977), 191--203. MR 585316
- [Sul1]
- {Sullivan:linefield}D.~Sullivan, {\em 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, Ann. of Math. Stud., vol. 97, PrincetonUniv. Press, Princeton, NJ, 1981. MR 624833
- [Sul2]
- {Sullivan:icm}\bysame {\em Quasiconformal homeomorphisms in dynamics, topology and geometry}, Proceedings of the International Conference of Mathematicians, 1986, vol. 2 Amer. Math. Soc., Providence, RI, 1986, pp. 1216--1228. MR 934326
- [Sul3]
- {Sullivan:renormalization}\bysame {\em Bounds, quadratic differentials and renormalization conjectures}, Mathematics into the Twenty-first Century, Amer. Math. Soc. Centennial Publications, vol. 2, Amer. Math., Soc., Providence, RI, 1992, pp. 417--466. MR 1184622
- [Th1]
- {Thurston:book}W.~P. Thurston, {\em Geometry and topology of three-manifolds}, Princeton lecture notes, 1979. MR
- [Th2]
- {Thurston:survey}\bysame {\em Three-dimensional manifolds, Kleinian groups and hyperbolic geometry}, Bull. Amer. Math. Soc. {\bf 6} (1982), 357--381. MR 648524
- [Th3]
- {Thurston:hype1}\bysame {\em Hyperbolic structures on \RM 3-manifolds \RM I\RM : Deformations of acylindrical manifolds},Ann. of Math. (2) {\bf 124} (1986), 203--246. MR 855294
- [Th4]
- {Thurston:mcg}\bysame {\em On the geometry and dynamics of diffeomorphisms of surfaces}, Bull. Amer. Math. Soc. {\bf 19} (1988), 417--432. MR 956596
- [Th5]
- {Thurston:hype2}\bysame {\em Hyperbolic structures on \RM 3-manifolds} II: {\em Surface groups and \RM 3-manifolds which fiber over the circle},Ann. of Math. (2) (to appear). MR
- [Th6]
- {Thurston:hype3}\bysame {\em Hyperbolic structures on \RM 3-manifolds} III: {\em Deformation of \RM 3-manifolds with incompressible boundary}, Ann. of Math. (2) (to appear). MR
- [Th7]
- {Thurston:hype4}\bysame {\em Hyperbolic structures on \RM 3-manifolds} IV: {\em Construction of hyperbolic manifolds}, in preparation. MR
- [Th8]
- {Thurston:rational}\bysame {\em On the combinatorics and dynamics of iterated rational maps},preprint. MR
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(2000):
57M99, 30C75
Retrieve articles in all Journals with MSC
(2000):
57M99, 30C75
Additional Information:
DOI:
10.1090/S0273-0979-1992-00313-0
PII:
S 0273-0979(1992)00313-0
|