Inventiones mathematicae

, Volume 118, Issue 1, pp 493–571

On the cone structure at infinity of Ricci flat manifolds with Euclidean volume growth and quadratic curvature decay

  • Jeff Cheeger
  • Gang Tian


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  1. [AA] F.J., Almgren, W.K. Allard: On the radial behaviour of minimal surfaces and the uniqueness of their tangent cones. Ann. Math.113 (1981) 215–265Google Scholar
  2. [A1] M., Anderson: Ricci curvature bounds and Einstein metrics on compact manifolds, Journal A.M.S.,2 (1989) 455–490Google Scholar
  3. [A2] M. Anderson: Convergence and rigidity of manifolds under Ricci curvature bounds. Invent. Math.,102 (1990) 429–445Google Scholar
  4. [AC1] M. Anderson, J. Cheeger: Finiteness theorems for manifolds with Ricci curvature andL n/2-norm of curvature bounded. J. Geom. Funct. Anal.,1 (1991) 231–252Google Scholar
  5. [AC2] M. Anderson, J. Cheeger,C α-compactness for manifolds with Ricci curvature and injectivity radius bounded below. J. Differ. Geom.3 (1992) 265–281Google Scholar
  6. [BKN] S. Bando, A. Kasue, H. Nakajima: On a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth. Invent. Math.,97 (1989) 313–349Google Scholar
  7. [BK] S. Bando, R. Kobayashi: Ricci flat Kähler metrics on affine algebraic manifolds, Geometry and Analysis on Manifolds, Lecture Notes in Math, Springer-Verlag (1987) 20–32Google Scholar
  8. [B] A. Besse: Einstein Manifolds. Ergeb. Math. Grenzgeb. Band 10, Springer, Berlin New York, 1987Google Scholar
  9. [C1] J. Cheeger: On the geometry of spaces with cone-like singularities. Proc. Nat. Acad. Sci.76 (1979) 2103–2106Google Scholar
  10. [C2] J. Cheeger: Analytic torsion and the heat equation. Ann. Math.109 (1979) 259–322Google Scholar
  11. [C3] J. Cheeger: Spectral geometry of singular Riemannian spaces. J. Diff. Geom.18 (1983) 575–657Google Scholar
  12. [CC1] J. Cheeger, T. Colding: Almost rigidity of warped products and the structure of spaces with Ricci curvature bounded below C.R. Acad. Sci. Paris (to appear)Google Scholar
  13. [CC2] J. Cheeger, T. Colding: Lower bounds on Ricci curvature and the almost rigidity of warped products (preprint)Google Scholar
  14. [CC3] J. Cheeger, T. Colding: On the structure of spaces with Ricci curvature bounded below (to appear)Google Scholar
  15. [CT] J. Cheeger, G. Tian (to appear)Google Scholar
  16. [E] D. Ebin: The manifold of riemannian metrics. A.M.S. Proc. Sym in Pure Math. Vol XV, Global Analysis (1970) 11–40Google Scholar
  17. [EM] D. Ebin, J. Marsden: Groups of Diffeomorphisms and the Motion of an Incompressible Fluid. Ann. Math. (22)92 (1970) 102–163Google Scholar
  18. [DNP] D.J. Duff, B.E.W. Wilson, C. Pope: Kaluzo-Klein Supergravity. Phys. Reports130 102–163 (1986)Google Scholar
  19. [G] L. Gao: Convergence of Riemannian manifolds. Ricci pinching andL n/2 curvature pinching. Jour. Diff. Geom32 (1990) 349–381Google Scholar
  20. [GT] D. Gilbarg, N. Trudinger: Elliptic Partial Differential Equations of Second Order. Springer, New York, 1977Google Scholar
  21. [GH] P. Griffiths. J Harris, Principles of algebraic geometry. Wiley, New York 1978Google Scholar
  22. [GPL] M. Gromov, J. Lafontaine, P. Pansu: Structures Métriques Pour Les Variétés Riemanniennes. Cedic/Fernand, Nathen 1981Google Scholar
  23. [N] A. Nadel: Multiplier Ideal Sheaves and Existence of Kähler-Einstein Metrics of Positive Scalar Curvature. Proc. Natl. Acad. Sci. USA86 (1989)Google Scholar
  24. [P] G. Perelman, (unpublished)Google Scholar
  25. [S1] L. Simon: Asymptotics for a Class of Non-linear Evolution Equations, With Applications to Geometric Problems. Ann. of Math.118 (1983) 525–571Google Scholar
  26. [S2] L. Simon: Springer Lecture Notes in Math. Springer-Verlag, 1161Google Scholar
  27. [T1] G. Tian: On Kähler-Einstein Metrics on Certain Kähler Manifolds WithC 1(M)>0. Invent. Math.89 (1987) 225–246Google Scholar
  28. [T2] G. Tian: On Calabi's Conjecture for Complex Surfaces With Positive First Chern Class. Invent. Math.101 (1990) 101–172Google Scholar
  29. [TY] G. Tian, S.T. Yau: Complete Kähler Manifolds With Zero Ricci Curvature, II. Invent. Math.106 (1991) 27–60Google Scholar
  30. [Y] D. Yang:L p Pinching and Compactness Theorems for Compactness Riemannian Manifolds. Séminaire de théorie Spectral et Géométric, Chambéry-Grenoble, 1987–1988) 81–89Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Jeff Cheeger
    • 1
  • Gang Tian
    • 1
  1. 1.Courant Institute of MathematicsNew YorkUSA

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