메뉴 건너뛰기




Volumn 143, Issue 2, 1996, Pages 331-355

Dimension and rigidity of quasi-Fuchsian representations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0030547969     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/2118646     Document Type: Article
Times cited : (29)

References (46)
  • 1
    • 0001684131 scopus 로고
    • A general form of the covering principle and relative differentiation of additive functions
    • A. S. BESICOVIC, A general form of the covering principle and relative differentiation of additive functions, Proc. Cambridge Phil. Soc. 41 (1945), 103-110.
    • (1945) Proc. Cambridge Phil. Soc. , vol.41 , pp. 103-110
    • Besicovic, A.S.1
  • 2
    • 51249186941 scopus 로고
    • Hausdorff dimension of quasi-circles
    • R. BOWEN, Hausdorff dimension of quasi-circles, Publ. Math. IHES 50 (1979), 11-25.
    • (1979) Publ. Math. IHES , vol.50 , pp. 11-25
    • Bowen, R.1
  • 3
    • 0000202395 scopus 로고
    • Sur le groupe de la géométrie hypersphérique
    • E. CARTAN, Sur le groupe de la géométrie hypersphérique, Comm. Math. Helv. 4 (1932), 158-171.
    • (1932) Comm. Math. Helv. , vol.4 , pp. 158-171
    • Cartan, E.1
  • 4
    • 0001189006 scopus 로고
    • Archimedean superrigidity and hyperbolic geometry
    • K. CORLETTE, Archimedean superrigidity and hyperbolic geometry, Ann. of Math. 135 (1992), 165-182.
    • (1992) Ann. of Math. , vol.135 , pp. 165-182
    • Corlette, K.1
  • 5
    • 84972517967 scopus 로고
    • Flat G-bundles with canonical metrics
    • _, Flat G-bundles with canonical metrics, J. Diff. Geom. 28 (1988), 361-382.
    • (1988) J. Diff. Geom. , vol.28 , pp. 361-382
  • 6
    • 0010987455 scopus 로고
    • Holomorphic immersions between compact hyperbolic space forms
    • H. D. CAO and N. MOK, Holomorphic immersions between compact hyperbolic space forms, Inv. Math. 100 (1990), 49-61.
    • (1990) Inv. Math. , vol.100 , pp. 49-61
    • Cao, H.D.1    Mok, N.2
  • 7
    • 0039208480 scopus 로고
    • Harmonic maps from compact Kähler manifolds to exceptional hyperbolic spaces
    • J. A. CARLSON and L. HERNÁNDEZ Harmonic maps from compact Kähler manifolds to exceptional hyperbolic spaces, J. Geom. Anal. 1 (1991), 339-357.
    • (1991) J. Geom. Anal. , vol.1 , pp. 339-357
    • Carlson, J.A.1    Hernández, L.2
  • 8
    • 51249177821 scopus 로고
    • Harmonic mapping of Kähler manifolds to locally symmetric spaces
    • J. A. CARLSON and D. TOLEDO, Harmonic mapping of Kähler manifolds to locally symmetric spaces, Publ. Math. IHES 69 (1989), 173-201.
    • (1989) Publ. Math. IHES , vol.69 , pp. 173-201
    • Carlson, J.A.1    Toledo, D.2
  • 13
    • 0000960125 scopus 로고
    • Proper holomorphic maps: A survey
    • J. E. Fornæss (ed.), Mathematical Notes, Princeton University Press
    • F. FORSTNERIČ, Proper holomorphic maps: a survey, Several Complex Variables, pp. 297-363, J. E. Fornæss (ed.), Mathematical Notes, Princeton University Press, 1993.
    • (1993) Several Complex Variables , pp. 297-363
    • Forstnerič, F.1
  • 14
    • 0040393073 scopus 로고
    • Geometrically finite groups, Patterson-Sullivan measures and Ratner's rigidity theorem
    • L. FLAMINIO and R. SPATZIER, Geometrically finite groups, Patterson-Sullivan measures and Ratner's rigidity theorem, Inv. Math. 99 (1990), 601-626.
    • (1990) Inv. Math. , vol.99 , pp. 601-626
    • Flaminio, L.1    Spatzier, R.2
  • 17
    • 0003195390 scopus 로고
    • Hyperbolic groups
    • MSRI publ. 8. Springer
    • _, Hyperbolic groups, pp. 75-263, in Essays in Group Theory, MSRI publ. 8. Springer, 1987.
    • (1987) Essays in Group Theory , pp. 75-263
  • 18
    • 0002771917 scopus 로고
    • The definitions and exceptional sets for quasi-conformal mappings
    • F. W. GEHRING, The definitions and exceptional sets for quasi-conformal mappings, Ann. Acad. Sci. Fenn. A. I. 281 (1960), 1-28.
    • (1960) Ann. Acad. Sci. Fenn. A. I. , vol.281 , pp. 1-28
    • Gehring, F.W.1
  • 19
    • 0002559391 scopus 로고
    • Pinching constants for hyperbolic manifolds
    • M. GROMOV and W. THURSTON, Pinching constants for hyperbolic manifolds, Inv. Math. 89 (1987), 1-12.
    • (1987) Inv. Math. , vol.89 , pp. 1-12
    • Gromov, M.1    Thurston, W.2
  • 20
    • 0000211188 scopus 로고
    • Local rigidity of discrete groups acting on complex hyperbolic space
    • W. M. GOLDMAN and J. J. MILLSON, Local rigidity of discrete groups acting on complex hyperbolic space, Inv. Math. 88 (1987), 495-520.
    • (1987) Inv. Math. , vol.88 , pp. 495-520
    • Goldman, W.M.1    Millson, J.J.2
  • 23
    • 0002506313 scopus 로고
    • Entropy-rigidity of locally symmetric spaces of negative curvature
    • U. HAMENSTÄDT, Entropy-rigidity of locally symmetric spaces of negative curvature, Ann. of Math. 131 (1990), 35-51.
    • (1990) Ann. of Math. , vol.131 , pp. 35-51
    • Hamenstädt, U.1
  • 24
    • 84974000364 scopus 로고
    • Kähler manifolds and 1/4-pinching
    • L. HERNÁNDEZ, Kähler manifolds and 1/4-pinching, Duke Math. J. 62 (1991), 601-611.
    • (1991) Duke Math. J. , vol.62 , pp. 601-611
    • Hernández, L.1
  • 26
    • 0000197332 scopus 로고
    • Deformation spaces associated to compact hyperbolic manifolds
    • Discrete Groups in Geometry and Analysis (R. Howe ed.), Birkhauser, Boston
    • D. JOHNSON and J. J. MILLSON, Deformation spaces associated to compact hyperbolic manifolds, pp. 48-106, in Discrete Groups in Geometry and Analysis (R. Howe ed.), Progress in Mathematics, vol. 67, Birkhauser, Boston, 1987.
    • (1987) Discrete Groups in Geometry and Analysis , vol.67 , pp. 48-106
    • Johnson, D.1    Millson, J.J.2
  • 27
    • 0040987115 scopus 로고
    • Harmonic maps and group representations
    • (B. Lawson & K. Temenblat, eds.), Longman Scientific
    • J. JOST and S. T. YAU, Harmonic maps and group representations, pp. 241-260, Differential Geometry and Minimal Submanifolds (B. Lawson & K. Temenblat, eds.), Longman Scientific, 1991.
    • (1991) Differential Geometry and Minimal Submanifolds , pp. 241-260
    • Jost, J.1    Yau, S.T.2
  • 28
    • 0000608218 scopus 로고
    • Entropy and closed geodesics
    • A. KATOK, Entropy and closed geodesics, Ergod. Th. & Dyn. Sys. 2 (1982), 339-367.
    • (1982) Ergod. Th. & Dyn. Sys. , vol.2 , pp. 339-367
    • Katok, A.1
  • 29
    • 84974277573 scopus 로고
    • Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations
    • M. KANAI, Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations, Ergod. Th. & Dyn. Sys. 8 (1988), 215-239.
    • (1988) Ergod. Th. & , vol.8 , pp. 215-239
    • Kanai, M.1    Dyn, S.2
  • 31
    • 0009025080 scopus 로고
    • Geodesic flows on symmetric Riemannian spaces
    • F. I. MAUTNER, Geodesic flows on symmetric Riemannian spaces, Ann. of Math. 65 (1957), 416-431.
    • (1957) Ann. of Math. , vol.65 , pp. 416-431
    • Mautner, F.I.1
  • 33
    • 51249188297 scopus 로고
    • Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms
    • _, Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms, Publ. Math. IHES 34 (1968), 53-104.
    • (1968) Publ. Math. IHES , vol.34 , pp. 53-104
  • 34
    • 0002077679 scopus 로고
    • Geometric superrigidity
    • N. MOK, Y. T. SIU and S. K. YEUNG, Geometric superrigidity, Inv. Math. 113 (1993), 57-83.
    • (1993) Inv. Math. , vol.113 , pp. 57-83
    • Mok, N.1    Siu, Y.T.2    Yeung, S.K.3
  • 35
    • 0001684717 scopus 로고
    • n: Distribution, rectifibility, and densities
    • n: distribution, rectifibility, and densities, Ann. of Math. 125 (1987), 537-643.
    • (1987) Ann. of Math. , vol.125 , pp. 537-643
    • Preiss, D.1
  • 36
    • 0001773527 scopus 로고
    • Métriques de Carnot-Carathéodory et quasi-isométries des espaces symétrique de range 1
    • P. PANSU, Métriques de Carnot-Carathéodory et quasi-isométries des espaces symétrique de range 1, Ann. of Math. 129 (1989), 1-60.
    • (1989) Ann. of Math. , vol.129 , pp. 1-60
    • Pansu, P.1
  • 37
    • 0000324012 scopus 로고
    • Dimension conforme et sphere à l'infini des variétés à courburé négative
    • _, Dimension conforme et sphere à L'infini des variétés à courburé négative, Ann. Acad. Sci. Fenn A. I. 14 (1989), 177-212.
    • (1989) Ann. Acad. Sci. Fenn A. I. , vol.14 , pp. 177-212
  • 38
    • 84974336812 scopus 로고
    • An example of an amenable action from geometry
    • R. SPATZIER, An example of an amenable action from geometry, Erg. Th. & Dyn. Syst. 7 (1987) 289-293.
    • (1987) Erg. Th. & Dyn. Syst. , vol.7 , pp. 289-293
    • Spatzier, R.1
  • 39
    • 0040987110 scopus 로고    scopus 로고
    • Private communication
    • S. SEMMES, Private communication.
    • Semmes, S.1
  • 40
    • 0000696637 scopus 로고
    • Quasiconformal homeomorphisms and dynamics. II. Structural stability implies hyperbolicity for Kleinian groups
    • D. SULLIVAN, Quasiconformal homeomorphisms and dynamics. II. Structural stability implies hyperbolicity for Kleinian groups, Acta Math. 155 (1985), 243-260.
    • (1985) Acta Math. , vol.155 , pp. 243-260
    • Sullivan, D.1
  • 41
    • 84966243904 scopus 로고
    • Discrete conformal groups and measurable dynamics
    • _, Discrete conformal groups and measurable dynamics, Bull. AMS 6 (1982), 57-73.
    • (1982) Bull. AMS , vol.6 , pp. 57-73
  • 42
    • 0000144097 scopus 로고
    • Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups
    • _, Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Math. 153 (1984), 259-277.
    • (1984) Acta Math. , vol.153 , pp. 259-277
  • 43
    • 0000978179 scopus 로고
    • A rigidity theorem for Möbius groups
    • P. TUKIA, A rigidity theorem for Möbius groups, Inv. Math. 97 (1989), 405-431.
    • (1989) Inv. Math. , vol.97 , pp. 405-431
    • Tukia, P.1
  • 45
    • 0040987117 scopus 로고    scopus 로고
    • Mostow rigidity of rank 1 discrete subgroups with ergodic Bowen-Margulis measure
    • to appear
    • C. B. YUE, Mostow rigidity of rank 1 discrete subgroups with ergodic Bowen-Margulis measure, to appear in Inv. Math.
    • Inv. Math.
    • Yue, C.B.1
  • 46
    • 0039472982 scopus 로고    scopus 로고
    • Negatively 1/4-pinched riemannian metric on a compact Kähler manifold
    • S. T. YAU and F. ZHENG, Negatively 1/4-pinched riemannian metric on a compact Kähler manifold, Inv. Math. 103, 527-535.
    • Inv. Math. , vol.103 , pp. 527-535
    • Yau, S.T.1    Zheng, F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.