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Volumn 355, Issue 5, 2003, Pages 1933-1959

Ricci flatness of asymptotically locally Euclidean metrics

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EID: 0037407183     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-02-03242-7     Document Type: Article
Times cited : (10)

References (47)
  • 1
    • 0000046378 scopus 로고
    • Lower curvature bounds, Toponogov's theorem, and bounded topology
    • [Ab] MR 87j:53058
    • [Ab] U. Abresch, Lower curvature bounds, Toponogov's theorem, and bounded topology, Ann. Sci. École Norm. Sup. 18 (1985), 651-670. MR 87j:53058
    • (1985) Ann. Sci. École Norm. Sup. , vol.18 , pp. 651-670
    • Abresch, U.1
  • 3
    • 0001215942 scopus 로고
    • On a construction of coordinates at infinity on manifolds with faster curvature decay and maximum volume growth
    • [B-K-N] MR 90c:53098
    • [B-K-N] S. Bando, A. Kasue and H. Nakajima, On a construction of coordinates at infinity on manifolds with faster curvature decay and maximum volume growth, Invent. Math. 97 (1989), 313-349. MR 90c:53098
    • (1989) Invent. Math. , vol.97 , pp. 313-349
    • Bando, S.1    Kasue, A.2    Nakajima, H.3
  • 4
    • 84990556234 scopus 로고
    • The mass of an asymptotically flat manifold
    • [Ba] MR 88b:58144
    • [Ba] R. Bartnik, The mass of an asymptotically flat manifold, Comm. Pure Appl. Math. 34 (1986), 661-693. MR 88b:58144
    • (1986) Comm. Pure Appl. Math. , vol.34 , pp. 661-693
    • Bartnik, R.1
  • 5
    • 0004058055 scopus 로고
    • [Be] Springer-Verlag, Berlin, MR 88f:53087
    • [Be] A. Besse, Einstein Manifolds, Springer-Verlag, Berlin, 1987. MR 88f:53087
    • (1987) Einstein Manifolds
    • Besse, A.1
  • 6
    • 33646029561 scopus 로고
    • The Dirichlet problem for a complex Mange-Ampère equation
    • [B-T] MR 56:3351
    • [B-T] E. Bedford and B. A. Taylor, The Dirichlet problem for a complex Mange-Ampère equation, Invent. Math. 37 (1976), 1-44. MR 56:3351
    • (1976) Invent. Math. , vol.37 , pp. 1-44
    • Bedford, E.1    Taylor, B.A.2
  • 7
    • 0000592268 scopus 로고
    • Métriques kählériennes et fibrés holomorphes
    • [C] MR 83m:32033
    • [C] E. Calabi, Métriques kählériennes et fibrés holomorphes, Ann. Sci. École Norm. Sup. 12 (1979), 269-294. MR 83m:32033
    • (1979) Ann. Sci. École Norm. Sup. , vol.12 , pp. 269-294
    • Calabi, E.1
  • 8
    • 84972500359 scopus 로고
    • The splitting theorem for manifolds of nonnegative Ricci curvature
    • [C-G] MR 46:2597
    • [C-G] J. Cheeger and D. Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Diff. Geom. 6 (1971/72), 119-128. MR 46:2597
    • (1971) J. Diff. Geom. , vol.6 , pp. 119-128
    • Cheeger, J.1    Gromoll, D.2
  • 10
    • 84980189206 scopus 로고
    • Differential equations on Riemannian manifolds and their geometric applications
    • [C-Y] MR 52:6608
    • [C-Y] S. Y. Cheng and S.-T. Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), 333-354. MR 52:6608
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 333-354
    • Cheng, S.Y.1    Yau, S.-T.2
  • 12
    • 38149143997 scopus 로고
    • Asymptotically flat manifolds of nonnegative curvature
    • [Ds] MR 95e:53052
    • [Ds] G. Drees, Asymptotically flat manifolds of nonnegative curvature, Differential Geom. Appl. 4 (1994), 77-90. MR 95e:53052
    • (1994) Differential Geom. Appl. , vol.4 , pp. 77-90
    • Drees, G.1
  • 13
    • 0002130829 scopus 로고
    • Asymptotically flat self-dual solutions to Euclidean gravity
    • [E-H] MR 80h:83011
    • [E-H] T. Eguchi and A. J. Hanson, Asymptotically flat self-dual solutions to Euclidean gravity, Ann. Physics 120 (1979), 82-106. MR 80h:83011
    • (1979) Ann. Physics , vol.120 , pp. 82-106
    • Eguchi, T.1    Hanson, A.J.2
  • 14
    • 0001635666 scopus 로고
    • Gravitational multi-instantons
    • [G-H]
    • [G-H] G.-W Gibbons and S. Hawking, Gravitational multi-instantons, Phys. Lett. B78 (1978), 430-432.
    • (1978) Phys. Lett. , vol.B78 , pp. 430-432
    • Gibbons, G.-W.1    Hawking, S.2
  • 15
    • 0000321857 scopus 로고
    • Über modifikationen und exzeptionelle analytische mengen
    • [Gt] MR 25:583
    • [Gt] H. Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962), 331-368. MR 25:583
    • (1962) Math. Ann. , vol.146 , pp. 331-368
    • Grauert, H.1
  • 16
    • 0013186966 scopus 로고    scopus 로고
    • A genealogy of noncompact manifolds of nonnegative curvature: History and logic
    • [Ge]
    • [Ge] R. E. Greene, A genealogy of noncompact manifolds of nonnegative curvature: history and logic, Comparison geometry (1997), 99-134.
    • (1997) Comparison Geometry , pp. 99-134
    • Greene, R.E.1
  • 17
    • 84963009173 scopus 로고
    • Riemannian manifolds of faster-than-quadratic curvature decay
    • [G-P-Z] MR 95m:53054
    • [G-P-Z] R. E. Greene, P. Petersen and S.-H. Zhu, Riemannian manifolds of faster-than-quadratic curvature decay. Internat. Math. Res. Notices no. 9, 1994, pp. 363-377. MR 95m:53054
    • (1994) Internat. Math. Res. Notices , vol.9 , pp. 363-377
    • Greene, R.E.1    Petersen, P.2    Zhu, S.-H.3
  • 18
    • 0001474422 scopus 로고
    • Function theory on manifolds which possess a pole
    • [G-W1] Springer, Berlin, MR 81a:53002
    • [G-W 1] R. E. Greene and H. Wu, Function theory on manifolds which possess a pole, Lecture Notes in Mathematics, vol. 699, Springer, Berlin, 1979. MR 81a:53002
    • (1979) Lecture Notes in Mathematics , vol.699
    • Greene, R.E.1    Wu, H.2
  • 19
    • 0002754231 scopus 로고
    • ∞ approximations of convex, subharmonic, and plurisubharmonic functions
    • [G-W 2] MR 80m:53055
    • ∞ approximations of convex, subharmonic, and plurisubharmonic functions, Ann. Sci. École Norm. Sup. 12 (1979), 47-84. MR 80m:53055
    • (1979) Ann. Sci. École Norm. Sup. , vol.12 , pp. 47-84
    • Greene, R.E.1    Wu, H.2
  • 20
    • 84972577735 scopus 로고
    • Gap theorems for noncompact Riemannian manifolds
    • [G-W 3] MR 84m:53050
    • [G-W 3] R. E. Greene and H. Wu, Gap theorems for noncompact Riemannian manifolds, Duke Math. J. 49 (1982), 731-756. MR 84m:53050
    • (1982) Duke Math. J. , vol.49 , pp. 731-756
    • Greene, R.E.1    Wu, H.2
  • 22
    • 80053092371 scopus 로고
    • Polygons and gravitons
    • [H] MR 80h:53047
    • [H] N. Hitchin, Polygons and gravitons, Math. Proc. Cambridge Philos. Soc. 85 (1979), 465-476. MR 80h:53047
    • (1979) Math. Proc. Cambridge Philos. Soc. , vol.85 , pp. 465-476
    • Hitchin, N.1
  • 23
    • 0002309139 scopus 로고    scopus 로고
    • Asymptotically locally Euclidean metrics with holonomy SU(m)
    • [J] MR 2002i:53063
    • [J] D. Joyce, Asymptotically locally Euclidean metrics with holonomy SU(m), Annals of Global Analysis and Geometry 19 (2000), 55-73. MR 2002i:53063
    • (2000) Annals of Global Analysis and Geometry , vol.19 , pp. 55-73
    • Joyce, D.1
  • 24
    • 84972513539 scopus 로고
    • Gap theorems for minimal submanifolds of Euclidean space
    • [Ka] MR 87h:53084
    • [Ka] A. Kasue, Gap theorems for minimal submanifolds of Euclidean space, J. Math. Soc. Japan 38 (1986), 473-492. MR 87h:53084
    • (1986) J. Math. Soc. Japan , vol.38 , pp. 473-492
    • Kasue, A.1
  • 25
    • 84972578210 scopus 로고
    • Gap theorems for certain submanifolds of Euclidean spaces and hyperbolic space forms
    • [K-S] MR 89a:53072
    • [K-S] A. Kasue and K. Sugahara, Gap theorems for certain submanifolds of Euclidean spaces and hyperbolic space forms, Osaka J. Math. 24 (1987), 679-704. MR 89a:53072
    • (1987) Osaka J. Math. , vol.24 , pp. 679-704
    • Kasue, A.1    Sugahara, K.2
  • 26
    • 84972540623 scopus 로고
    • The construction of ALE spaces as hyper-Kähler quotients
    • [Kr] MR 90d:53055
    • [Kr] P. Kronheimer, The construction of ALE spaces as hyper-Kähler quotients, J. Diff. Geom. 29 (1989), 665-683. MR 90d:53055
    • (1989) J. Diff. Geom. , vol.29 , pp. 665-683
    • Kronheimer, P.1
  • 27
    • 84968518038 scopus 로고
    • The Yamabe problem
    • [L-P] MR 88f:53001
    • [L-P] J. Lee and T. Parker, The Yamabe problem, Bull. Amer. Math. Soc. 17 (1987), 37-91. MR 88f:53001
    • (1987) Bull. Amer. Math. Soc. , vol.17 , pp. 37-91
    • Lee, J.1    Parker, T.2
  • 28
    • 0040460276 scopus 로고
    • p and mean value properties of subharmonic functions on Riemannian manifolds
    • [L-S] MR 86j:58147
    • p and mean value properties of subharmonic functions on Riemannian manifolds, Acta Math. 153 (1984), 279-301. MR 86j:58147
    • (1984) Acta Math. , vol.153 , pp. 279-301
    • Li, P.1    Schoen, R.2
  • 29
    • 0000324115 scopus 로고
    • On the parabolic kernel of the Schrödinger operator
    • [L-Y] MR 87f:58156
    • [L-Y] P. Li and S.-T. Yau, On the parabolic kernel of the Schrödinger operator, Acta Math. 156 (1986), 153-201. MR 87f:58156
    • (1986) Acta Math. , vol.156 , pp. 153-201
    • Li, P.1    Yau, S.-T.2
  • 30
    • 0001952156 scopus 로고
    • Regular points for elliptic equations with discontinuous coefficients
    • [L-S-W] MR 28:4228
    • [L-S-W] W. Littman, G. Stampacchia and H. F. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa 17 (1963), 43-77. MR 28:4228
    • (1963) Ann. Scuola Norm. Sup. Pisa , vol.17 , pp. 43-77
    • Littman, W.1    Stampacchia, G.2    Weinberger, H.F.3
  • 31
    • 0000478901 scopus 로고
    • An embedding theorem of complete Kähler manifolds of positive bisectional curvature onto affine algebraic varieties
    • [Mk] MR 87a:53103
    • [Mk] N. Mok, An embedding theorem of complete Kähler manifolds of positive bisectional curvature onto affine algebraic varieties, Bull. Soc. Math. France 112 (1984), 197-250. MR 87a:53103
    • (1984) Bull. Soc. Math. France , vol.112 , pp. 197-250
    • Mok, N.1
  • 32
    • 0013184926 scopus 로고    scopus 로고
    • Minimal submanifolds with finite total scalar curvature
    • [Me] MR 98e:58053
    • [Me] H. Moore, Minimal submanifolds with finite total scalar curvature, Indiana Univ. Math. Jour. 45 (1996), 1021-1043. MR 98e:58053
    • (1996) Indiana Univ. Math. Jour. , vol.45 , pp. 1021-1043
    • Moore, H.1
  • 34
    • 84980080977 scopus 로고
    • On Harnack's theorem for elliptic differential equations
    • [Mr] MR 28:2356
    • [Mr] J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577-591. MR 28:2356
    • (1961) Comm. Pure Appl. Math. , vol.14 , pp. 577-591
    • Moser, J.1
  • 36
    • 0000331198 scopus 로고
    • The Poincaré-Lelong equation on complete Kähler manifolds
    • [M-S-Y] MR 84g:32011
    • [M-S-Y] N. Mok, Y.-T. Siu and S.-T. Yau, The Poincaré-Lelong equation on complete Kähler manifolds, Compositio Math. 44 (1981), 183-218. MR 84g:32011
    • (1981) Compositio Math. , vol.44 , pp. 183-218
    • Mok, N.1    Siu, Y.-T.2    Yau, S.-T.3
  • 37
    • 0004102184 scopus 로고
    • [M-K] Holt, Rinehart and Winston, New York. MR 46:2080
    • [M-K] J. A. Morrow and K. Kodaira, Complex manifolds, Holt, Rinehart and Winston, New York, 1971. MR 46:2080
    • (1971) Complex Manifolds
    • Morrow, J.A.1    Kodaira, K.2
  • 38
    • 34250956285 scopus 로고
    • The Levi problem for complex spaces
    • [Na] MR 26:6439
    • [Na] R. Narasimhan, The Levi problem for complex spaces, Math. Ann. 142 (1960/1961), 335-365. MR 26:6439
    • (1960) Math. Ann. , vol.142 , pp. 335-365
    • Narasimhan, R.1
  • 39
    • 0032172091 scopus 로고    scopus 로고
    • Vanishing theorems on complete Kähler manifolds and their applications
    • [N] MR 2000c:32069
    • [N] L. Ni, Vanishing theorems on complete Kähler manifolds and their applications, J. Differential Geom. 50 (1998), 89-122. MR 2000c:32069
    • (1998) J. Differential Geom. , vol.50 , pp. 89-122
    • Ni, L.1
  • 40
    • 0000467661 scopus 로고    scopus 로고
    • Poisson equation, Poincaré-Lelong equation and curvature decay on complete Kähler manifolds
    • [N-S-T] MR 2002j:53042
    • [N-S-T] L. Ni, Y.-G. Shi and L.-F. Tam, Poisson equation, Poincaré-Lelong equation and curvature decay on complete Kähler manifolds, J. Diff. Geom. 57 (2001), 339-388. MR 2002j:53042
    • (2001) J. Diff. Geom. , vol.57 , pp. 339-388
    • Ni, L.1    Shi, Y.-G.2    Tam, L.-F.3
  • 41
    • 0030635298 scopus 로고    scopus 로고
    • Ricci flow and the uniformization on complete noncompact Kähler manifolds
    • [S] MR 98d:53099
    • [S] W.-X. Shi, Ricci flow and the uniformization on complete noncompact Kähler manifolds. J. Differential Geom. 45 (1997), 94-220. MR 98d:53099
    • (1997) J. Differential Geom. , vol.45 , pp. 94-220
    • Shi, W.-X.1
  • 42
    • 29244463784 scopus 로고
    • Proof of the positive mass theorem, II
    • [Sc-Y] MR 831:83045
    • [Sc-Y] R. Schoen and S.-T. Yau, Proof of the positive mass theorem, II, Comm. Math. Phys. 79 (1981), 231-260. MR 831:83045
    • (1981) Comm. Math. Phys. , vol.79 , pp. 231-260
    • Schoen, R.1    Yau, S.-T.2
  • 43
    • 0000796692 scopus 로고
    • Complete Kähler manifolds with nonpositive curvature faster than quadratic decay
    • [Si-Y] MR 55:10719
    • [Si-Y] Y.-T. Siu and S.-T. Yau, Complete Kähler manifolds with nonpositive curvature faster than quadratic decay, Annals of Math. 105 (1977), 225-264. MR 55:10719
    • (1977) Annals of Math. , vol.105 , pp. 225-264
    • Siu, Y.-T.1    Yau, S.-T.2
  • 44
    • 21844510693 scopus 로고
    • Liouville properties of harmonic maps
    • [T] MR 96k:58063
    • [T] L.-F. Tam, Liouville properties of harmonic maps, Math. Res. Lett. 2 (1995), 719-735. MR 96k:58063
    • (1995) Math. Res. Lett. , vol.2 , pp. 719-735
    • Tam, L.-F.1
  • 45
    • 0002498432 scopus 로고
    • Complete Kähler manifolds with zero Ricci curvature II
    • [T-Y] MR 92j:32028
    • [T-Y] G. Tian and S.-T. Yau, Complete Kähler manifolds with zero Ricci curvature II, Invent. Math. 106 (1991), 27-60. MR 92j:32028
    • (1991) Invent. Math. , vol.106 , pp. 27-60
    • Tian, G.1    Yau, S.-T.2
  • 46
    • 84980178548 scopus 로고
    • Harmonic functions on complete Riemannian manifolds
    • [Y] MR 55:4042
    • [Y] S.-T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201-228. MR 55:4042
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 201-228
    • Yau, S.-T.1
  • 47
    • 51249179272 scopus 로고
    • Complete Kähler manifolds of positive Ricci curvature
    • [Yg] MR 91h:53065
    • [Yg] S.-K. Yeung, Complete Kähler manifolds of positive Ricci curvature, Math. Z. 204 (1990), 187-208. MR 91h:53065
    • (1990) Math. Z. , vol.204 , pp. 187-208
    • Yeung, S.-K.1


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