메뉴 건너뛰기




Volumn 41, Issue 2, 2002, Pages 341-361

On Mostow rigidity for variable negative curvature

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0242307354     PISSN: 00409383     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0040-9383(00)00040-9     Document Type: Article
Times cited : (5)

References (53)
  • 1
    • 0001799360 scopus 로고
    • Uber eine verallgemeinerung der riemannschen geometrie
    • MR:19,304h
    • A.D. Alexandrov, Uber eine Verallgemeinerung der Riemannschen Geometrie, Schriften Forschungsinst. Math, 1 (1957) 33-84, MR:19,304h.
    • (1957) Schriften Forschungsinst. Math. , vol.1 , pp. 33-84
    • Alexandrov, A.D.1
  • 2
    • 0000832854 scopus 로고
    • Convergence and rigidity of manifolds under Ricci curvature bounds
    • M.T. Anderson, Convergence and rigidity of manifolds under Ricci curvature bounds, Invent. Math. 102 (2) (1990) 429-445.
    • (1990) Invent. Math. , vol.102 , Issue.2 , pp. 429-445
    • Anderson, M.T.1
  • 4
    • 0032172435 scopus 로고    scopus 로고
    • Counting open negatively curved manifolds up to tangential homotopy equivalence
    • I. Belegradek, Counting open negatively curved manifolds up to tangential homotopy equivalence, J. Differential Geom. 50 (1) (1998) 59-88.
    • (1998) J. Differential Geom. , vol.50 , Issue.1 , pp. 59-88
    • Belegradek, I.1
  • 6
    • 22644452304 scopus 로고    scopus 로고
    • Lipschitz precompactness for closed negatively curved manifolds
    • I. Belegradek, Lipschitz precompactness for closed negatively curved manifolds, Proc. Amer. Math. Soc. 127 (4) (1999) 1201-1208.
    • (1999) Proc. Amer. Math. Soc. , vol.127 , Issue.4 , pp. 1201-1208
    • Belegradek, I.1
  • 7
    • 84972527232 scopus 로고
    • Pincement riemannien et pincement holomorphe
    • M. Berger, Pincement riemannien et pincement holomorphe, Ann. Scuola Norm. Sup. Pisa 14 (3) (1960) 151-159.
    • (1960) Ann. Scuola Norm. Sup. Pisa , vol.14 , Issue.3 , pp. 151-159
    • Berger, M.1
  • 9
    • 0000168310 scopus 로고
    • Entropies et rigidités des espaces localement symétriques de courbure strictement négative
    • G. Besson, G. Courtois, S. Gallot, Entropies et rigidités des espaces localement symétriques de courbure strictement négative, Geom. Funct. Anal. 5 (5) (1995) 731-799.
    • (1995) Geom. Funct. Anal. , vol.5 , Issue.5 , pp. 731-799
    • Besson, G.1    Courtois, G.2    Gallot, S.3
  • 11
    • 84972583778 scopus 로고
    • Degenerations of the hyperbolic space
    • M. Bestvina, Degenerations of the hyperbolic space, Duke Math. J. 56 (1988) 143-161.
    • (1988) Duke Math. J. , vol.56 , pp. 143-161
    • Bestvina, M.1
  • 12
    • 0001103575 scopus 로고
    • Stable actions of groups on real trees
    • M. Bestvina, M. Feighn, Stable actions of groups on real trees, Invent. Math. 121 (2) (1995) 287-321.
    • (1995) Invent. Math. , vol.121 , Issue.2 , pp. 287-321
    • Bestvina, M.1    Feighn, M.2
  • 13
    • 0002416737 scopus 로고
    • Some implications of the generalized Gauss-Bonnet theorem
    • R.L. Bishop, S.I. Goldberg, Some implications of the generalized Gauss-Bonnet theorem, Trans. Amer. Math. Soc. 112 (1964) 508-535.
    • (1964) Trans. Amer. Math. Soc. , vol.112 , pp. 508-535
    • Bishop, R.L.1    Goldberg, S.I.2
  • 14
    • 0032061199 scopus 로고    scopus 로고
    • Smooth structures on collarable ends of 4-manifolds
    • Ž. Bižaca, J. Etnyre, Smooth structures on collarable ends of 4-manifolds, Topology 37 (3) (1998) 461-467.
    • (1998) Topology , vol.37 , Issue.3 , pp. 461-467
    • Bižaca, Ž.1    Etnyre, J.2
  • 15
    • 84972492349 scopus 로고
    • Discrete parabolic groups
    • B.H. Bowditch, Discrete parabolic groups, J. Differential Geom. 38 (1993) 559-583.
    • (1993) J. Differential Geom. , vol.38 , pp. 559-583
    • Bowditch, B.H.1
  • 16
    • 84973999883 scopus 로고
    • Geometrical finiteness with variable negative curvature
    • B.H. Bowditch, Geometrical finiteness with variable negative curvature, Duke Math. J. 77 (1995) 229-274.
    • (1995) Duke Math. J. , vol.77 , pp. 229-274
    • Bowditch, B.H.1
  • 19
    • 0013524664 scopus 로고
    • Amenable groups and stabilizers of measures on the boundary of a Hadamard manifold
    • M. Burger, V. Schroeder, Amenable groups and stabilizers of measures on the boundary of a Hadamard manifold, Math. Ann. 276 (3) (1987) 505-514.
    • (1987) Math. Ann. , vol.276 , Issue.3 , pp. 505-514
    • Burger, M.1    Schroeder, V.2
  • 20
    • 0001302746 scopus 로고
    • On the characteristic numbers of complete manifolds of bounded curvature and finite volume
    • Springer, Berlin
    • J. Cheeger, M. Gromov, On the characteristic numbers of complete manifolds of bounded curvature and finite volume, Differential Geometry and Complex Analysis, Springer, Berlin, 1985, pp. 115-154.
    • (1985) Differential Geometry and Complex Analysis , pp. 115-154
    • Cheeger, J.1    Gromov, M.2
  • 21
    • 0005591936 scopus 로고
    • On curvature and characteristic classes of a Riemann manifold
    • S.S. Chern, On curvature and characteristic classes of a Riemann manifold, Abh. Math. Sem. Univ. Hamburg 20 (1955) 117-126, in book: Shiing-Shen Chern selected papers, Vol. II, Springer, Berlin, 1989.
    • (1955) Abh. Math. Sem. Univ. Hamburg , vol.20 , pp. 117-126
    • Chern, S.S.1
  • 22
    • 0005591936 scopus 로고
    • book, Springer, Berlin
    • S.S. Chern, On curvature and characteristic classes of a Riemann manifold, Abh. Math. Sem. Univ. Hamburg 20 (1955) 117-126, in book: Shiing-Shen Chern selected papers, Vol. II, Springer, Berlin, 1989.
    • (1989) Shiing-Shen Chern Selected Papers , vol.2
  • 23
    • 0004247206 scopus 로고
    • Grundlehren der mathematische Wissenshaften, Springer, Berlin
    • A. Dold, in: Lectures on Algebraic Topology, Grundlehren der mathematische Wissenshaften, Vol. 200, Springer, Berlin, 1972.
    • (1972) Lectures on Algebraic Topology , vol.200
    • Dold, A.1
  • 24
    • 0039472972 scopus 로고
    • Complex hyperbolic manifolds and exotic smooth structures
    • F.T. Farrell, L.E. Jones, Complex hyperbolic manifolds and exotic smooth structures, Invent. Math. 117 (1) (1989) 57-74.
    • (1989) Invent. Math. , vol.117 , Issue.1 , pp. 57-74
    • Farrell, F.T.1    Jones, L.E.2
  • 25
    • 84968484221 scopus 로고
    • Negatively curved manifolds with exotic smooth structures
    • F.T. Farrell, L.E. Jones, Negatively curved manifolds with exotic smooth structures, J. Amer. Math. Soc. 2 (4) (1989) 899-908.
    • (1989) J. Amer. Math. Soc. , vol.2 , Issue.4 , pp. 899-908
    • Farrell, F.T.1    Jones, L.E.2
  • 26
    • 84972513478 scopus 로고
    • Nonuniform hyperbolic lattices and exotic smooth structures
    • F.T. Farrell, L.E. Jones, Nonuniform hyperbolic lattices and exotic smooth structures, J. Differential Geom. 38 (2) (1993) 235-261.
    • (1993) J. Differential Geom. , vol.38 , Issue.2 , pp. 235-261
    • Farrell, F.T.1    Jones, L.E.2
  • 27
    • 0002022139 scopus 로고
    • Topological rigidity for compact non-positively curved manifolds
    • Amer. Math. Soc., Providence, RI
    • F.T. Farrell, L.E. Jones, Topological rigidity for compact non-positively curved manifolds, Proc. Sympos. Pure Math. Vol. 54, Part 3, Amer. Math. Soc., Providence, RI, 1993, pp. 229-274.
    • (1993) Proc. Sympos. Pure Math. , vol.54 , Issue.PART 3 , pp. 229-274
    • Farrell, F.T.1    Jones, L.E.2
  • 29
    • 0000675796 scopus 로고    scopus 로고
    • Hyperbolic manifolds with negatively curved exotic triangulations in dimensions greater than five
    • F.T. Farrell, L.E. Jones, P. Ontaneda, Hyperbolic manifolds with negatively curved exotic triangulations in dimensions greater than five, J. Differential Geom. 48 (2) (1998) 319-322.
    • (1998) J. Differential Geom. , vol.48 , Issue.2 , pp. 319-322
    • Farrell, F.T.1    Jones, L.E.2    Ontaneda, P.3
  • 30
    • 0010022288 scopus 로고
    • 4-Manifold topology. I. Subexponential groups
    • M.H. Freedman, P. Teichner, 4-manifold topology. I. Subexponential groups, Invent. Math. 122 (3) (1995) 509-529.
    • (1995) Invent. Math. , vol.122 , Issue.3 , pp. 509-529
    • Freedman, M.H.1    Teichner, P.2
  • 31
    • 84972537530 scopus 로고
    • A finiteness theorem for negatively curved manifolds
    • K. Fukaya, A finiteness theorem for negatively curved manifolds, J. Differential Geom. 20 (2) (1984) 497-521.
    • (1984) J. Differential Geom. , vol.20 , Issue.2 , pp. 497-521
    • Fukaya, K.1
  • 32
    • 0000054796 scopus 로고
    • Theory of convergence for Riemannian orbifolds
    • K. Fukaya, Theory of convergence for Riemannian orbifolds, Japan. J. Math. (N.S.) 12 (1) (1986) 121-160.
    • (1986) Japan. J. Math. (N.S.) , vol.12 , Issue.1 , pp. 121-160
    • Fukaya, K.1
  • 33
    • 84972492906 scopus 로고
    • n/2-curvature pinching
    • n/2-curvature pinching, J. Differential Geom. 32 (2) (1990) 349-381.
    • (1990) J. Differential Geom. , vol.32 , Issue.2 , pp. 349-381
    • Gao, L.Z.1
  • 34
    • 84972530202 scopus 로고
    • Manifolds of negative curvature
    • M. Gromov, Manifolds of negative curvature, J. Differential Geom. 13 (2) (1978) 223-230.
    • (1978) J. Differential Geom. , vol.13 , Issue.2 , pp. 223-230
    • Gromov, M.1
  • 36
    • 0002559391 scopus 로고
    • Pinching constants for hyperbolic manifolds
    • M. Gromov, W. Thurston, Pinching constants for hyperbolic manifolds, Invent. Math. 89 (1987) 1-12.
    • (1987) Invent. Math. , vol.89 , pp. 1-12
    • Gromov, M.1    Thurston, W.2
  • 37
    • 84966202446 scopus 로고
    • An open collar theorem for 4-manifolds
    • C.R. Guilbault, An open collar theorem for 4-manifolds, Trans. Amer. Math. Soc. 331 (1) (1992) 227-245.
    • (1992) Trans. Amer. Math. Soc. , vol.331 , Issue.1 , pp. 227-245
    • Guilbault, C.R.1
  • 39
    • 0009943421 scopus 로고
    • Smoothings of Piecewise linear manifolds
    • Princeton University Press, Princeton, NJ
    • M. Hirsch, B. Mazur, Smoothings of Piecewise Linear Manifolds, Annals of Mathematics Studies, Vol. 80, Princeton University Press, Princeton, NJ, 1974.
    • (1974) Annals of Mathematics Studies , vol.80
    • Hirsch, M.1    Mazur, B.2
  • 40
    • 0003251147 scopus 로고
    • Foundational essays on topological manifolds, smoothings, and triangulations
    • Princeton University Press, Princeton, NJ
    • R.S. Kirby, L.S. Siebenmann, Foundational Essays on Topological Manifolds, Smoothings, and Triangulations, Annals of Mathematics Studies, Vol. 88, Princeton University Press, Princeton, NJ, 1977.
    • (1977) Annals of Mathematics Studies , vol.88
    • Kirby, R.S.1    Siebenmann, L.S.2
  • 42
    • 0002137498 scopus 로고
    • Einstein metrics and Mostow rigidity
    • C. LeBrun, Einstein metrics and Mostow rigidity, Math. Res. Lett. 2 (1) (1995) 1-8.
    • (1995) Math. Res. Lett. , vol.2 , Issue.1 , pp. 1-8
    • LeBrun, C.1
  • 43
    • 0001396385 scopus 로고
    • Kähler surface of negative curvature not covered by the ball
    • G.D. Mostow, Y.T. Siu, A compact Kähler surface of negative curvature not covered by the ball, Ann. Math. 112 (1980) 321-360.
    • (1980) Ann. Math. , vol.112 , pp. 321-360
    • Mostow, G.D.1    Siu, Y.T.2    Compact, A.3
  • 44
    • 10644272883 scopus 로고
    • Closure of the set of classical Riemannian spaces
    • I.G. Nikolaev, Closure of the set of classical Riemannian spaces, J. Soviet Math. 55 (6) (1991) 2100-2115.
    • (1991) J. Soviet Math. , vol.55 , Issue.6 , pp. 2100-2115
    • Nikolaev, I.G.1
  • 45
    • 0002832883 scopus 로고
    • Topologie de Gromov équivariante, structures hyperboliques et arbres réels
    • F. Paulin, Topologie de Gromov équivariante, structures hyperboliques et arbres réels, Invent. Math. 94 (1) (1988) 53-80.
    • (1988) Invent. Math. , vol.94 , Issue.1 , pp. 53-80
    • Paulin, F.1
  • 46
    • 0000482872 scopus 로고
    • Outer automorphisms of hyperbolic groups and small actions on ℝ-trees
    • R.C. Alperin (Ed.), Math. Sci. Res. Inst. Publ., Springer, Berlin
    • F. Paulin, Outer automorphisms of hyperbolic groups and small actions on ℝ-trees, in: R.C. Alperin (Ed.), Arboreal Group Theory, Math. Sci. Res. Inst. Publ., Vol. 19, Springer, Berlin, 1991, pp. 331-343.
    • (1991) Arboreal Group Theory , vol.19 , pp. 331-343
    • Paulin, F.1
  • 47
    • 0009277178 scopus 로고
    • Discrete subgroups isomorphic to lattices in semisimple lie groups
    • G. Prasad, Discrete subgroups isomorphic to lattices in semisimple lie groups, Amer. J. Math. 98 (1) (1976) 241-261.
    • (1976) Amer. J. Math. , vol.98 , Issue.1 , pp. 241-261
    • Prasad, G.1
  • 49
    • 0001580237 scopus 로고
    • Structure and rigidity in hyperbolic groups I
    • E. Rips, Z. SeLa, Structure and rigidity in hyperbolic groups I, Geom. Funct. Anal. 4 (3) (1994) 337-371.
    • (1994) Geom. Funct. Anal. , vol.4 , Issue.3 , pp. 337-371
    • Rips, E.1    SeLa, Z.2
  • 50
    • 84972500085 scopus 로고
    • Finite volume and fundamental group on manifolds of negative curvature
    • V. Schroeder, Finite volume and fundamental group on manifolds of negative curvature, J. Differential Geom. 20 (1) (1984) 175-183.
    • (1984) J. Differential Geom. , vol.20 , Issue.1 , pp. 175-183
    • Schroeder, V.1
  • 51
    • 0004211763 scopus 로고
    • Springer, Berlin
    • J.-P. Serre, Trees, Springer, Berlin, 1980.
    • (1980) Trees
    • Serre, J.-P.1
  • 52
    • 0001924496 scopus 로고
    • On irreducible 3-manifolds which are sufficiently large
    • F. Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. Math. 87 (1968) 56-88.
    • (1968) Ann. Math. , vol.87 , pp. 56-88
    • Waldhausen, F.1
  • 53
    • 0038819206 scopus 로고
    • Uniformization of 1/4-pinched negatively curved manifolds with special holonomy
    • S.-K. Yeung, Uniformization of 1/4-pinched negatively curved manifolds with special holonomy, Internat. Math. Res. Notices (8) (1995) 365-375.
    • (1995) Internat. Math. Res. Notices , Issue.8 , pp. 365-375
    • Yeung, S.-K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.