메뉴 건너뛰기




Volumn 171, Issue 1, 2010, Pages 1-107

The classification of Kleinian surface groups, I: models and bounds

Author keywords

[No Author keywords available]

Indexed keywords


EID: 77952720063     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2010.171.1     Document Type: Review
Times cited : (161)

References (64)
  • 1
    • 74249102795 scopus 로고
    • Kleinian groups-geometrically finite and geometrically perverse
    • Amer. Math. Soc., Providence, RI
    • W. Abikoff, Kleinian groups-geometrically finite and geometrically perverse, in Geometry of Group Representations (Boulder, CO, 1987), Contemp. Math. 74, Amer. Math. Soc., Providence, RI, 1988, pp. 1-50.
    • (1988) Geometry of Group Representations (Boulder, CO, 1987), Contemp. Math , vol.74 , pp. 1-50
    • Abikoff, W.1
  • 3
    • 0001190134 scopus 로고
    • Riemann's mapping theorem for variable metrics
    • L. Ahlfors and L. Bers, Riemann's mapping theorem for variable metrics, Ann. of Math. 72 (1960), 385-404.
    • (1960) Ann. of Math. , vol.72 , pp. 385-404
    • Ahlfors, L.1    Bers, L.2
  • 4
    • 0000553024 scopus 로고
    • Finitely generated Kleinian groups
    • L. V. Ahlfors, Finitely generated Kleinian groups, Amer. J. Math. 86 (1964), 413-429.
    • (1964) Amer. J. Math. , vol.86 , pp. 413-429
    • Ahlfors, L.V.1
  • 5
    • 0002928014 scopus 로고
    • Notes on word hyperbolic groups
    • World Sci. Publ., River Edge, NJ, (H. Short, ed.)
    • J. M. Alonso and ET AL., Notes on word hyperbolic groups, in Group Theory from a Geometrical Viewpoint (Trieste, 1990), World Sci. Publ., River Edge, NJ, 1991, (H. Short, ed.), pp. 3-63.
    • (1991) Group Theory from a Geometrical Viewpoint (Trieste, 1990) , pp. 3-63
    • Alonso, J.M.1
  • 6
    • 0000946208 scopus 로고    scopus 로고
    • Cores of hyperbolic 3-manifolds and limits of Kleinian groups
    • J. W. Anderson and R. D. Canary, Cores of hyperbolic 3-manifolds and limits of Kleinian groups, Amer. J. Math. 118 (1996), 745-779.
    • (1996) Amer. J. Math. , vol.118 , pp. 745-779
    • Anderson, J.W.1    Canary, R.D.2
  • 8
    • 0002979611 scopus 로고
    • Simultaneous uniformization
    • L. Bers, Simultaneous uniformization, Bull. Amer. Math. Soc. 66 (1960), 94-97.
    • (1960) Bull. Amer. Math. Soc. , vol.66 , pp. 94-97
    • Bers, L.1
  • 9
    • 0001146280 scopus 로고
    • On boundaries of Teichmüller spaces and on Kleinian groups
    • L. Bers, On boundaries of Teichmüller spaces and on Kleinian groups. I, Ann. of Math. 91 (1970), 570-600.
    • (1970) I, Ann. of Math. , vol.91 , pp. 570-600
    • Bers, L.1
  • 12
    • 0002861269 scopus 로고
    • An inequality for Riemann surfaces
    • Springer-Verlag, New York
    • L. Bers, An inequality for Riemann surfaces, in Differential Geometry and Complex Analysis, Springer-Verlag, New York, 1985, pp. 87-93.
    • (1985) Differential Geometry and Complex Analysis , pp. 87-93
    • Bers, L.1
  • 13
    • 0002437863 scopus 로고
    • Bouts des variétés hyperboliques de dimension 3
    • F. Bonahon, Bouts des variétés hyperboliques de dimension 3, Ann. of Math. 124 (1986), 71-158.
    • (1986) Ann. of Math. , vol.124 , pp. 71-158
    • Bonahon, F.1
  • 15
    • 0002672089 scopus 로고
    • Notes on Gromov's hyperbolicity criterion for path-metric spaces
    • World Sci. Publ., River Edge, NJ
    • B. H. Bowditch, Notes on Gromov's hyperbolicity criterion for path-metric spaces, in Group Theory from a Geometrical Viewpoint (Trieste, 1990), World Sci. Publ., River Edge, NJ, 1991, pp. 64-167.
    • (1991) Group Theory from a Geometrical Viewpoint (Trieste, 1990) , pp. 64-167
    • Bowditch, B.H.1
  • 16
    • 77952709987 scopus 로고    scopus 로고
    • End invariants of hyperbolic 3-manifolds, preprint
    • B. H. Bowditch, End invariants of hyperbolic 3-manifolds, preprint, 2005.
    • (2005)
    • Bowditch, B.H.1
  • 17
    • 0034366797 scopus 로고    scopus 로고
    • Continuity of Thurston's length function
    • J. F. Brock, Continuity of Thurston's length function, Geom. Funct. Anal. 10 (2000), 741-797.
    • (2000) Geom. Funct. Anal. , vol.10 , pp. 741-797
    • Brock, J.F.1
  • 19
    • 84972562390 scopus 로고
    • Collars in Kleinian groups
    • R. Brooks and J. P. Matelski, Collars in Kleinian groups, Duke Math. J. 49 (1982), 163-182.
    • (1982) Duke Math. J. , vol.49 , pp. 163-182
    • Brooks, R.1    Matelski, J.P.2
  • 21
    • 33645827794 scopus 로고    scopus 로고
    • Shrinkwrapping and the taming of hyperbolic 3-manifolds
    • D. Calegari and D. Gabai, Shrinkwrapping and the taming of hyperbolic 3-manifolds, J. Amer. Math. Soc. 19 (2006), 385-446.
    • (2006) J. Amer. Math. Soc. , vol.19 , pp. 385-446
    • Calegari, D.1    Gabai, D.2
  • 23
    • 84968484274 scopus 로고
    • Ends of hyperbolic 3-manifolds
    • R. D. Canary, Ends of hyperbolic 3-manifolds, J. Amer. Math. Soc. 6 (1993), 1-35.
    • (1993) J. Amer. Math. Soc. , vol.6 , pp. 1-35
    • Canary, R.D.1
  • 27
    • 77952734119 scopus 로고
    • (Papers from the Swiss Seminar on Hyperbolic Groups held in Bern
    • E. Ghys and P. De La Harpe (eds.) Birkhäuser, Boston, MA, 1990
    • E. Ghys and P. De La Harpe (eds.), Sur les Groupes Hyperboliques d'après Mikhael Gromov, Progr. Math. 83, Birkhäuser, Boston, MA, 1990, (Papers from the Swiss Seminar on Hyperbolic Groups held in Bern, 1988).
    • (1988) Sur les Groupes Hyperboliques d'après Mikhael Gromov, Progr. Math , vol.83
  • 30
    • 0001369661 scopus 로고
    • A presentation for the mapping class group of a closed orientable surface
    • A. Hatcher and W. Thurston, A presentation for the mapping class group of a closed orientable surface, Topology 19 (1980), 221-237.
    • (1980) Topology , vol.19 , pp. 221-237
    • Hatcher, A.1    Thurston, W.2
  • 32
    • 0000090033 scopus 로고
    • On discrete groups of Möbius transformations
    • T. Jørgensen, On discrete groups of Möbius transformations, Amer. J. Math. 98 (1976), 739-749.
    • (1976) Amer. J. Math. , vol.98 , pp. 739-749
    • Jørgensen, T.1
  • 33
    • 0039856455 scopus 로고
    • A proof of Selberg's conjecture
    • D. A. Kazhdan and G. A. Margulis, A proof of Selberg's conjecture, Math. USSR Sb. 4 (1968), 147-152.
    • (1968) Math. USSR Sb. , vol.4 , pp. 147-152
    • Kazhdan, D.A.1    Margulis, G.A.2
  • 36
    • 51249190645 scopus 로고
    • On spaces of Kleinian groups
    • I. Kra, On spaces of Kleinian groups, Comment. Math. Helv. 47 (1972), 53-69.
    • (1972) Comment. Math. Helv. , vol.47 , pp. 53-69
    • Kra, I.1
  • 37
    • 38249024835 scopus 로고
    • On Ahlfors' finiteness theorem
    • R. S. Kulkarni and P. B. Shalen, On Ahlfors' finiteness theorem, Adv. Math. 76 (1989), 155-169.
    • (1989) Adv. Math. , vol.76 , pp. 155-169
    • Kulkarni, R.S.1    Shalen, P.B.2
  • 38
    • 0010679814 scopus 로고
    • On the isomorphism theorem for Kleinian groups
    • A. Marden and B. Maskit, On the isomorphism theorem for Kleinian groups, Invent. Math. 51 (1979), 9-14.
    • (1979) Invent. Math. , vol.51 , pp. 9-14
    • Marden, A.1    Maskit, B.2
  • 39
    • 0000954277 scopus 로고
    • The geometry of finitely generated Kleinian groups
    • A. Marden, The geometry of finitely generated Kleinian groups, Ann. of Math. 99 (1974), 383-462.
    • (1974) Ann. of Math. , vol.99 , pp. 383-462
    • Marden, A.1
  • 40
    • 0001064064 scopus 로고
    • Self-maps on Kleinian groups
    • B. Maskit, Self-maps on Kleinian groups, Amer. J. Math. 93 (1971), 840-856.
    • (1971) Amer. J. Math. , vol.93 , pp. 840-856
    • Maskit, B.1
  • 43
    • 0033473346 scopus 로고    scopus 로고
    • Geometry of the complex of curves
    • H. A. Masur, Geometry of the complex of curves. I. Hyperbolicity, Invent. Math. 138 (1999), 103-149.
    • (1999) I. Hyperbolicity, Invent. Math. , vol.138 , pp. 103-149
    • Masur, H.A.1
  • 44
    • 0000018142 scopus 로고
    • Compact submanifolds of 3-manifolds with boundary
    • D. Mccullough, Compact submanifolds of 3-manifolds with boundary, Quart. J. Math. Oxford Ser. 37 (1986), 299-307.
    • (1986) Quart. J. Math. Oxford Ser. , vol.37 , pp. 299-307
    • Mccullough, D.1
  • 45
    • 0000937731 scopus 로고
    • A lower bound for the volume of hyperbolic 3-manifolds
    • R. Meyerhoff, A lower bound for the volume of hyperbolic 3-manifolds, Canad. J. Math. 39 (1987), 1038-1056.
    • (1987) Canad. J. Math. , vol.39 , pp. 1038-1056
    • Meyerhoff, R.1
  • 46
    • 0009122729 scopus 로고    scopus 로고
    • A geometric approach to the complex of curves on a surface
    • World Sci. Publ., River Edge, NJ
    • Y. N. Minsky, A geometric approach to the complex of curves on a surface, in Topology and Teichmüller Spaces (Katinkulta, 1995), World Sci. Publ., River Edge, NJ, 1996, pp. 149-158.
    • (1996) Topology and Teichmüller Spaces (Katinkulta, 1995) , pp. 149-158
    • Minsky, Y.N.1
  • 47
    • 0033468108 scopus 로고    scopus 로고
    • The Classification of punctured-torus groups
    • Y. N. Minsky, The Classification of punctured-torus groups, Ann. of Math. 149 (1999), 559-626.
    • (1999) Ann. of Math. , vol.149 , pp. 559-626
    • Minsky, Y.N.1
  • 48
    • 0041062645 scopus 로고    scopus 로고
    • Kleinian groups and the complex of curves
    • Y. N. Minsky, Kleinian groups and the complex of curves, Geom. Topol. 4 (2000), 117-148.
    • (2000) Geom. Topol. , vol.4 , pp. 117-148
    • Minsky, Y.N.1
  • 49
    • 0035637007 scopus 로고    scopus 로고
    • Bounded geometry for Kleinian groups
    • Y. N. Minsky, Bounded geometry for Kleinian groups, Invent. Math. 146 (2001), 143-192.
    • (2001) Invent. Math. , vol.146 , pp. 143-192
    • Minsky, Y.N.1
  • 50
    • 0000427353 scopus 로고
    • Concerning upper semi-continuous collections of continua
    • R. L. Moore, Concerning upper semi-continuous collections of continua, Trans. Amer. Math. Soc. 27 (1925), 416-428.
    • (1925) Trans. Amer. Math. Soc. , vol.27 , pp. 416-428
    • Moore, R.L.1
  • 51
    • 3042852212 scopus 로고
    • On the foundations of plane analysis situs
    • R. L. Moore, On the foundations of plane analysis situs, Trans. Amer. Math. Soc. 17 (1916), 131-164.
    • (1916) Trans. Amer. Math. Soc. , vol.17 , pp. 131-164
    • Moore, R.L.1
  • 52
    • 51249188297 scopus 로고
    • Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms
    • G. D. Mostow, Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math. (1968), 53-104.
    • (1968) Inst. Hautes Études Sci. Publ. Math. , pp. 53-104
    • Mostow, G.D.1
  • 54
    • 0001743192 scopus 로고
    • Strong rigidity of Q-rank 1 lattices
    • G. Prasad, Strong rigidity of Q-rank 1 lattices, Invent. Math. 21 (1973), 255-286.
    • (1973) Invent. Math. , vol.21 , pp. 255-286
    • Prasad, G.1
  • 55
    • 77952702442 scopus 로고    scopus 로고
    • The ending laminations theorem direct from Teichmüller geodesics
    • M. Rees, The ending laminations theorem direct from Teichmüller geodesics, 2004. arXiv math.
    • (2004)
    • Rees, M.1
  • 56
    • 84959841963 scopus 로고
    • Compact submanifolds of 3-manifolds
    • G. P. Scott, Compact submanifolds of 3-manifolds, J. London Math. Soc. 7 (1973), 246-250.
    • (1973) J. London Math. Soc. , vol.7 , pp. 246-250
    • Scott, G.P.1
  • 61
    • 84966239529 scopus 로고
    • Three-dimensional manifolds, Kleinian groups and hyperbolic geometry
    • W. P. Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. 6 (1982), 357-381.
    • (1982) Bull. Amer. Math. Soc. , vol.6 , pp. 357-381
    • Thurston, W.P.1
  • 62
    • 0001182097 scopus 로고
    • Hyperbolic structures on 3-manifolds. I. Deformation of acylindrical manifolds
    • W. P. Thurston, Hyperbolic structures on 3-manifolds. I. Deformation of acylindrical manifolds, Ann. of Math. 124 (1986), 203-246.
    • (1986) Ann. of Math. , vol.124 , pp. 203-246
    • Thurston, W.P.1
  • 63
    • 77951466870 scopus 로고    scopus 로고
    • Princeton Univ. Press, Princeton, NJ (Silvio Levy, ed.)
    • W. P. Thurston, Three-Dimensional Geometry and Topology. Vol. 1, Princeton Math. Series 35, Princeton Univ. Press, Princeton, NJ, 1997 (Silvio Levy, ed.).
    • (1997) Three-Dimensional Geometry and Topology , vol.1 , pp. 35
    • Thurston, W.P.1
  • 64
    • 0001902456 scopus 로고
    • Möbius transformations in several dimensions
    • P. L. Waterman, Möbius transformations in several dimensions, Adv. Math. 101 (1993), 87-113.
    • (1993) Adv. Math. , vol.101 , pp. 87-113
    • Waterman, P.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.