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Volumn 5, Issue 3, 1997, Pages 199-269

Extrema of curvature functionals on the space of metrics on 3-manifolds

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EID: 0000035404     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005260050066     Document Type: Article
Times cited : (49)

References (58)
  • 1
    • 0003796630 scopus 로고
    • [Ad] Academic Press, N.Y.
    • [Ad] R. Adams, Sobolev Spaces, Academic Press, N.Y. (1975)
    • (1975) Sobolev Spaces
    • Adams, R.1
  • 3
    • 0000832854 scopus 로고
    • Convergence and rigidity of manifolds under Ricci curvature bounds
    • [An1]
    • [An1] M. Anderson, Convergence and rigidity of manifolds under Ricci curvature bounds, Inventiones Math. 102, (1990), 429-445
    • (1990) Inventiones Math. , vol.102 , pp. 429-445
    • Anderson, M.1
  • 4
    • 84974003890 scopus 로고
    • Remarks on the compactness of isospectral sets in low dimensions
    • [An2]
    • [An2] M. Anderson, Remarks on the compactness of isospectral sets in low dimensions. Duke Math. Jour. 63, (1991), 699-711
    • (1991) Duke Math. Jour. , vol.63 , pp. 699-711
    • Anderson, M.1
  • 5
    • 0002891326 scopus 로고
    • Degenerations of metrics with bounded curvature and applications to critical metrics of Riemannian functionals
    • [An3]
    • [An3] M. Anderson, Degenerations of metrics with bounded curvature and applications to critical metrics of Riemannian functionals, Proc. Symp. Pure Math., Amer. Math. Soc. 53:3 (1993), 53-79
    • (1993) Proc. Symp. Pure Math., Amer. Math. Soc. , vol.53 , Issue.3 , pp. 53-79
    • Anderson, M.1
  • 6
    • 0002217693 scopus 로고
    • Scalar curvature and geometrization conjectures for 3-manifolds
    • [An] MSRI Publ.
    • [An] M. Anderson, Scalar curvature and geometrization conjectures for 3-manifolds, Comparison Geometry, MSRI Publ. 30, (1991), 47-80
    • (1991) Comparison Geometry , vol.30 , pp. 47-80
    • Anderson, M.1
  • 7
    • 84972511806 scopus 로고
    • α compactness for manifolds with Ricci curvature and injectivity radius bounded below
    • [AC]
    • α compactness for manifolds with Ricci curvature and injectivity radius bounded below. Jour. Diff. Geom. 35, (1992), 265-281
    • (1992) Jour. Diff. Geom. , vol.35 , pp. 265-281
    • Anderson, M.1    Cheeger, J.2
  • 8
    • 84972500378 scopus 로고
    • Metriques Riemanniennes et courbure
    • [Au1]
    • [Au1] T. Aubin, Metriques Riemanniennes et courbure, Jour. Differential Geometry 4, (1970), 383-124
    • (1970) Jour. Differential Geometry , vol.4 , pp. 383-1124
    • Aubin, T.1
  • 9
    • 0001596880 scopus 로고
    • Equations differentielles nonlineares et probleme de Yamabe concernant la courbure scalaire
    • [Au2]
    • [Au2] T. Aubin, Equations differentielles nonlineares et probleme de Yamabe concernant la courbure scalaire, J. Math. Pures Appl. 55, (1976), 269-296
    • (1976) J. Math. Pures Appl. , vol.55 , pp. 269-296
    • Aubin, T.1
  • 10
    • 0003255464 scopus 로고
    • Nonlinear Analysis on Manifolds. Monge-Ampere Equations
    • [Au3] Springer Verlag
    • [Au3] T. Aubin, Nonlinear Analysis on Manifolds. Monge-Ampere Equations, Grundlehren Series 252, Springer Verlag, (1982)
    • (1982) Grundlehren Series , vol.252
    • Aubin, T.1
  • 11
  • 12
    • 0011623919 scopus 로고
    • Quelques formules de variation pour une structure Riemannienne
    • [Ber]
    • [Ber] M. Berger, Quelques formules de variation pour une structure Riemannienne, Ann. Sci. Ecole Norm. Sup. 3, (1970), 285-294
    • (1970) Ann. Sci. Ecole Norm. Sup. , vol.3 , pp. 285-294
    • Berger, M.1
  • 14
    • 0039805990 scopus 로고
    • Les varietes hyperboliques sont des minima de l'entropie topologique
    • [BCG]
    • [BCG] G. Besson, G. Courtois and S. Gallot, Les varietes hyperboliques sont des minima de l'entropie topologique, Inventiones Math. 117, (1994), 403-445
    • (1994) Inventiones Math. , vol.117 , pp. 403-445
    • Besson, G.1    Courtois, G.2    Gallot, S.3
  • 15
    • 0002818931 scopus 로고
    • Finiteness theorems for Riemannian manifolds
    • [C]
    • [C] J. Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92, (1970), 61-74
    • (1970) Amer. J. Math. , vol.92 , pp. 61-74
    • Cheeger, J.1
  • 16
    • 84972538920 scopus 로고
    • Collapsing Riemannian manifolds while keeping their curvature bounded 1
    • [CG1]
    • [CG1] J. Cheeger, M. Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded 1, Jour. Differential Geometry 23, (1986), 309-346
    • (1986) Jour. Differential Geometry , vol.23 , pp. 309-346
    • Cheeger, J.1    Gromov, M.2
  • 17
    • 84972508732 scopus 로고
    • Collapsing Riemannian manifolds while keeping their curvature bounded 11
    • [CG2]
    • [CG2] J. Cheeger, M. Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded 11, Jour. Differential Geometry 32, (1990), 269-298
    • (1990) Jour. Differential Geometry , vol.32 , pp. 269-298
    • Cheeger, J.1    Gromov, M.2
  • 18
    • 0001302746 scopus 로고
    • On the characteristic numbers of complete manifolds of bounded curvature and finite volume
    • [CG3] Chavel, Farkas, Eds., Springer Verlag, New York
    • [CG3] J. Cheeger, M. Gromov, On the characteristic numbers of complete manifolds of bounded curvature and finite volume, H. Rauch Mem. Vol 1, (Chavel, Farkas, Eds.), Springer Verlag, New York, (1985), 115-154
    • (1985) H. Rauch Mem. , vol.1 , pp. 115-154
    • Cheeger, J.1    Gromov, M.2
  • 20
    • 0002984718 scopus 로고
    • The manifold of Riemannian metrics
    • [E]
    • [E] D. Ebin, The manifold of Riemannian metrics, Proc. Symp. Pure Math, A.M.S. 15, (1968), 11-40
    • (1968) Proc. Symp. Pure Math, A.M.S. , vol.15 , pp. 11-40
    • Ebin, D.1
  • 21
    • 0002162376 scopus 로고
    • Metric deformations of curvature 1
    • [Eh]
    • [Eh] P. Ehrlich, Metric deformations of curvature 1, Geometriae Ded. 5, (1976), 1-23
    • (1976) Geometriae Ded. , vol.5 , pp. 1-23
    • Ehrlich, P.1
  • 22
    • 0003212014 scopus 로고
    • An Introduction to Partial Differential Equations
    • [Fo] Princeton Univ. Press, Princeton
    • [Fo] G. Folland, An Introduction to Partial Differential Equations, Mathematical Notes, Princeton Univ. Press, Princeton, (1976)
    • (1976) Mathematical Notes
    • Folland, G.1
  • 23
    • 84972541450 scopus 로고
    • Collapsing Riemannian manifolds to ones of lower dimensions
    • [Fu]
    • [Fu] K. Fukaya, Collapsing Riemannian manifolds to ones of lower dimensions. Jour. Diff. Geom. 25, (1987), 139-156
    • (1987) Jour. Diff. Geom. , vol.25 , pp. 139-156
    • Fukaya, K.1
  • 24
    • 0000038293 scopus 로고
    • Isoperimetric inequalities based on integral norms of Ricci curvature
    • [Ga]
    • [Ga] S. Gallot, Isoperimetric inequalities based on integral norms of Ricci curvature. Asterisque 157-158, (1988), 191-216
    • (1988) Asterisque , vol.157-158 , pp. 191-216
    • Gallot, S.1
  • 26
    • 84972568148 scopus 로고
    • Lipschitz convergence of Riemannian manifolds
    • [GW]
    • [GW] R. Greene, H. Wu, Lipschitz convergence of Riemannian manifolds, Pacific J. Math. 131, (1988), 119-141
    • (1988) Pacific J. Math. , vol.131 , pp. 119-141
    • Greene, R.1    Wu, H.2
  • 28
    • 0002344449 scopus 로고
    • Volume and bounded cohomology
    • [Gr2]
    • [Gr2] M. Gromov, Volume and bounded cohomology, Publ. Math. I.H.E.S 56, (1982), 5-100
    • (1982) Publ. Math. I.H.E.S , vol.56 , pp. 5-100
    • Gromov, M.1
  • 29
    • 84951610586 scopus 로고
    • Positive scalar curvature and the Dirac operator on complete Riemannian manifolds
    • [GL]
    • [GL] M. Gromov, B. Lawson, Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publ. Math. I.H.E.S. 58, (1983), 83-196
    • (1983) Publ. Math. I.H.E.S. , vol.58 , pp. 83-196
    • Gromov, M.1    Lawson, B.2
  • 31
    • 84973998790 scopus 로고
    • Compactness of conformal metrics with integral bounds on curvature
    • [Gu]
    • [Gu] M. Gursky, Compactness of conformal metrics with integral bounds on curvature, Duke Math. Jour. 72, (1993), 339-367
    • (1993) Duke Math. Jour. , vol.72 , pp. 339-367
    • Gursky, M.1
  • 32
    • 84972513449 scopus 로고
    • Three manifolds with positive Ricci curvature
    • [H]
    • [H] R. Hamilton, Three manifolds with positive Ricci curvature. Jour. Diff. Geom. 17, (1982), 255-306
    • (1982) Jour. Diff. Geom. , vol.17 , pp. 255-306
    • Hamilton, R.1
  • 33
    • 84968516531 scopus 로고
    • A convergence theorem for Riemannian manifolds and some applications
    • [Ka]
    • [Ka] A. Kasue, A convergence theorem for Riemannian manifolds and some applications, Nagoya Math. J. 114, (1989), 21-51
    • (1989) Nagoya Math. J. , vol.114 , pp. 21-51
    • Kasue, A.1
  • 34
    • 0000851223 scopus 로고
    • Deformation to positive scalar curvature on complete manifolds
    • [Kaz]
    • [Kaz] J. Kazdan, Deformation to positive scalar curvature on complete manifolds, Math. Annalen 261, (1982), 227-234
    • (1982) Math. Annalen , vol.261 , pp. 227-234
    • Kazdan, J.1
  • 35
    • 0001399282 scopus 로고
    • Scalar curvature of a metric with unit volume
    • [Ko]
    • [Ko] O. Kobayashi, Scalar curvature of a metric with unit volume. Math. Annalen 279, (1987), 253-265
    • (1987) Math. Annalen , vol.279 , pp. 253-265
    • Kobayashi, O.1
  • 36
    • 3142588339 scopus 로고
    • [La] Thesis, S.U.N.Y. at Stony Brook
    • [La] F. Lamontagne, Thesis, S.U.N.Y. at Stony Brook, (1993)
    • (1993)
    • Lamontagne, F.1
  • 38
    • 21844503319 scopus 로고
    • Curvature h-principles
    • [Lo]
    • [Lo] J. Lohkamp, Curvature h-principles, Annals of Math. 142, (1995), 457-498
    • (1995) Annals of Math. , vol.142 , pp. 457-498
    • Lohkamp, J.1
  • 39
    • 0003212876 scopus 로고
    • Non-Homogeneous Boundary Value Problems and Applications 1
    • [LM] Springer Verlag, New York
    • [LM] J.L. Lions, E. Magenes, Non-Homogeneous Boundary Value Problems and Applications 1, Grundlehren Series 181, Springer Verlag, New York, (1972)
    • (1972) Grundlehren Series , vol.181
    • Lions, J.L.1    Magenes, E.2
  • 40
    • 0003246772 scopus 로고
    • Multiple Integrals in the Calculus of Variations
    • [Mo] Springer Verlag, New York
    • [Mo] C. Morrey, Jr., Multiple Integrals in the Calculus of Variations, Grundlehren Series 130, Springer Verlag, New York, (1966)
    • (1966) Grundlehren Series , vol.130
    • Morrey Jr., C.1
  • 41
    • 0003348894 scopus 로고
    • Seifert manifolds
    • [O] Springer Verlag, New York
    • [O] P. Orlik, Seifert manifolds, Lect. Notes in Math. 291, Springer Verlag, New York, 1972
    • (1972) Lect. Notes in Math. , vol.291
    • Orlik, P.1
  • 43
    • 0002158912 scopus 로고
    • Convergence of Riemannian manifolds
    • [Pe]
    • [Pe] S. Peters, Convergence of Riemannian manifolds, Compositio Math. 62, (1987), 3-16
    • (1987) Compositio Math. , vol.62 , pp. 3-16
    • Peters, S.1
  • 44
    • 3142627771 scopus 로고
    • [R1] Thesis, S.U.N.Y. at Stony Brook
    • [R1] X. Rong, Thesis, S.U.N.Y. at Stony Brook, (1990)
    • (1990)
    • Rong, X.1
  • 45
    • 84972498355 scopus 로고
    • The limiting eta invariant of collapsed 3-manifolds
    • [R2]
    • [R2] X. Rong, The limiting eta invariant of collapsed 3-manifolds, Jour. Diff. Geom. 37, (1993), 535-568
    • (1993) Jour. Diff. Geom. , vol.37 , pp. 535-568
    • Rong, X.1
  • 46
    • 84972506352 scopus 로고
    • Conformal deformation of a Riemannian metric to constant scalar curvature
    • [Sc1]
    • [Sc1] R. Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Diff. Geom. 20, (1984), 479-195
    • (1984) J. Diff. Geom. , vol.20 , pp. 479-1195
    • Schoen, R.1
  • 47
    • 0001107969 scopus 로고
    • Variational theory for the total scalar curvature functional for Riemannian metrics and related topics
    • [Sc2] Springer Verlag, Berlin
    • [Sc2] R. Schoen, Variational theory for the total scalar curvature functional for Riemannian metrics and related topics, Lect. Notes Math. 1365, Springer Verlag, Berlin, (1987), 120-154
    • (1987) Lect. Notes Math. , vol.1365 , pp. 120-154
    • Schoen, R.1
  • 48
    • 0001145921 scopus 로고
    • On the structure of manifolds with positive scalar curvature
    • [SY]
    • [SY] R. Schoen, S.T. Yau, On the structure of manifolds with positive scalar curvature, Manuscripta Math. 29, (1979), 159-183
    • (1979) Manuscripta Math. , vol.29 , pp. 159-183
    • Schoen, R.1    Yau, S.T.2
  • 49
    • 0038292676 scopus 로고
    • The geometries of 3-manifolds
    • [St]
    • [St] P. Scott, The geometries of 3-manifolds, Bulletin London Math. Soc. 15, (1983), 401-487
    • (1983) Bulletin London Math. Soc. , vol.15 , pp. 401-487
    • Scott, P.1
  • 51
    • 84966239529 scopus 로고
    • Three dimensional manifolds, Kleinian groups and hyperbolic geometry
    • [Th2]
    • [Th2] W. Thurston, Three dimensional manifolds, Kleinian groups and hyperbolic geometry. Bulletin A.M.S. 6, (1982), 357-381
    • (1982) Bulletin A.M.S. , vol.6 , pp. 357-381
    • Thurston, W.1
  • 52
    • 0000471156 scopus 로고
    • Remarks concerning the conformal deformation of Riemannian structures on compact manifolds
    • [Tr]
    • [Tr] N. Trudinger, Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa 22, (1968), 265-274
    • (1968) Ann. Scuola Norm. Sup. Pisa , vol.22 , pp. 265-274
    • Trudinger, N.1
  • 53
    • 0000952164 scopus 로고
    • Eine Klasse von 3-dimensionalen Mannigfaltigkeiten I, II
    • [Wa]
    • [Wa] F. Waldhausen, Eine Klasse von 3-dimensionalen Mannigfaltigkeiten I, II, Invent. Math. 3, (1967), 308-333, 4, (1967), 87-117
    • (1967) Invent. Math. , vol.3 , pp. 308-333
    • Waldhausen, F.1
  • 54
    • 34250521493 scopus 로고
    • [Wa] F. Waldhausen, Eine Klasse von 3-dimensionalen Mannigfaltigkeiten I, II, Invent. Math. 3, (1967), 308-333, 4, (1967), 87-117
    • (1967) Invent. Math. , vol.4 , pp. 87-117
  • 55
    • 84972561687 scopus 로고
    • On a deformation of Riemannian structures on compact manifolds
    • [Ym]
    • [Ym] H. Yamabe, On a deformation of Riemannian structures on compact manifolds, Osaka Math. J. 12, (1960), 21-37
    • (1960) Osaka Math. J. , vol.12 , pp. 21-37
    • Yamabe, H.1
  • 56
    • 0003111108 scopus 로고
    • Convergence of Riemannian manifolds with integral bounds on curvature I
    • [Yn1]
    • [Yn1] D. Yang, Convergence of Riemannian manifolds with integral bounds on curvature I, Ann. Sc. Ecole Norm. Sup. 25, (1992), 77-105
    • (1992) Ann. Sc. Ecole Norm. Sup. , vol.25 , pp. 77-105
    • Yang, D.1
  • 57
    • 84974003488 scopus 로고
    • Riemannian manifolds with small integral norm of curvature
    • [Yn2]
    • [Yn2] D. Yang, Riemannian manifolds with small integral norm of curvature. Duke Math. Jour. 65, (1992), 501-510
    • (1992) Duke Math. Jour. , vol.65 , pp. 501-510
    • Yang, D.1
  • 58
    • 84980178548 scopus 로고
    • Harmonic functions on complete Riemannian manifolds
    • [Ya]
    • [Ya] S.T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28, (1975), 201-228
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 201-228
    • Yau, S.T.1


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