Convergence of riemannian manifolds with integral bounds on curvature. I

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1. [1] M. T. ANDERSON, Ricci Curvature Bounds and Einstein Metrics on Compact Manifolds (J. Am. Math. Soc., 1989, pp. 455-490). Zbl0694.53045MR90g:53052
2. [2] M. T. ANDERSON, Convergence and Rigidity of Manifolds Under Ricci Curvature Bounds (Invent. Math., Vol. 102, 1990, pp. 429-445). Zbl0711.53038MR92c:53024
3. [3] M. T. ANDERSON and J. CHEEGER, Diffeomorphism Finiteness for Manifolds with Ricci Curvature and Ln/2-Norm of Curvature Bounded, preprint, 1990. 
4. [4] J. BEMELMANS, MIN-OO and E. A. RUH, Smoothing Riemannian Metrics (Math. Zeitschr., Vol. 188, 1984, pp. 69-74). Zbl0536.53044MR85m:58184
5. [5] P. BUSER and H. KARCHER, Gromov's Almost Flat Manifolds (Astérisque, Vol. 81, 1981). Zbl0459.53031MR83m:53070
6. [6] I. CHAVEL, Eigenvalues in Riemannian Geometry, Academic Press, 1984. Zbl0551.53001MR86g:58140
7. [7] J. CHEEGER, M. GROMOV and M. TAYLOR, Finite Propagation Speed, Kernel Estimates for Functions of the Laplace Operator and the Geometry of Complete Riemannian Manifolds (J. Diff. Geometry, Vol. 17, 1982, p. 15-53). Zbl0493.53035MR84b:58109
8. [8] J. CHEEGER, Finiteness Theorems for Riemannian Manifolds (Am. J. Math., Vol. 92, 1970, pp. 61-74). Zbl0194.52902MR41 #7697
9. [9] C. B. CROKE, Some Isoperimetric Inequalities and Eigenvalue Estimates (Ann. scient. Éc. Norm. Sup., Vol. 13, 1980, pp. 419-435). Zbl0465.53032MR83d:58068
10. [10] D. M. DETURCK, Deforming Metrics in the Direction of Their Ricci Tensors (J. Diff. Geometry, Vol. 18, 1983, pp. 157-162). Zbl0517.53044MR85j:53050
11. [11] S. GALLOT, Isoperimetric Inequalities Based on Integral Norms of Ricci Curvature (Astérisque, Vol. 157-158, 1988, pp. 191-216). Zbl0665.53041MR90a:58179
12. [12] L. ZHIYONG GAO, Convergence of Riemannian Manifolds, Ricci Pinching, and Ln/2-Curvature Pinching, (J. Diff. Geometry, Vol. 32, 1990, pp. 349-382). Zbl0752.53022
13. [13] L. ZHIYONG GAO, Einstein Manifolds (J. Diff. Geometry, Vol. 32, 1990, pp. 155-183). Zbl0719.53024
14. [14] L. ZHIYONG GAO, Ln/2-Curvature Pinching (J. Diff. Geometry, Vol. 32, 1990, pp. 713-774). Zbl0721.53039
15. [15] R. E. GREENE and HUNG-HSI WU, Lipschitz Convergence of Riemannian Manifolds, (Pac. J. Math., Vol. 131, 1988, pp. 119-141). Zbl0646.53038MR89g:53063
16. [16] M. GROMOV, J. LAFONTAINE and P. PANSU, Structures métriques pour les variétés riemanniennes, Cedic, 1981. Zbl0509.53034MR85e:53051
17. [17] R. S. HAMILTON, Three-Manifolds with Positive Ricci Curvature, (J. Diff. Geometry, Vol. 17, 1982, pp. 255-306). Zbl0504.53034MR84a:53050
18. [18] S. KLAINERMAN, Global Existence for Nonlinear Wave Equations (Commun. Pure Appl. Math., Vol. 43, 1980, pp. 43-101). Zbl0405.35056MR81b:35050
19. [19] S. PETERS, Convergence of Riemannian Manifolds (Compositio Mathematica, Vol. 62, 1987, pp. 3-16). Zbl0618.53036MR88i:53076
20. [20] WAN-XIONG SHI, Deforming the Metric on Complete Riemannian Manifolds, preprint, 1987. 
21. [21] M. E. TAYLOR, Pseudodifferential Operators, Princeton University Press, 1981. Zbl0453.47026MR82i:35172
22. [22] D. YANG, Convergence of Riemannian Manifolds with Integral Bounds on Curvature. II [Ann. scient. Éc. Norm. Sup. (to appear)]. Zbl0781.53035
23. [23] D. YANG, Lp Pinching and Compactness Theorems for Compact Riemannian Manifolds, preprint. 
24. [24] D. YANG, Riemannian Manifolds with Small Integral Norm of Curvature, preprint, 1989. 
25. [25] D. YANG, Existence and Regularity of Energy-Minimizing Riemannian Metrics [Internat. Math. Research Notices (Duke Math. J.), 1991]. Zbl0732.53036MR92f:58039

1. Erwann Aubry, Finiteness of ${\pi }_1$ and geometric inequalities in almost positive Ricci curvature
2. Deane Yang, Convergence of riemannian manifolds with integral bounds on curvature. II