@article{ASENS_2007_4_40_4_675_0, author = {Aubry, Erwann}, title = {Finiteness of ${\pi }\_{1}$ and geometric inequalities in almost positive Ricci curvature}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, volume = {40}, year = {2007}, pages = {675-695}, doi = {10.1016/j.ansens.2007.07.001}, zbl = {pre05219877}, language = {en}, url = {http://dml.mathdoc.fr/item/ASENS_2007_4_40_4_675_0} }
Aubry, Erwann. Finiteness of ${\pi }_{1}$ and geometric inequalities in almost positive Ricci curvature. Annales scientifiques de l'École Normale Supérieure, Tome 40 (2007) pp. 675-695. doi : 10.1016/j.ansens.2007.07.001. http://gdmltest.u-ga.fr/item/ASENS_2007_4_40_4_675_0/
[1] A theorem of Myers, Duke Math. J. 24 (1957) 345-348. | MR 89464 | Zbl 0078.14204
,[2] Aubry E., Variétés de courbure de Ricci presque minorée : inégalités géométriques optimales et stabilité des variétés extrémales, Thèse, Institut Fourier, Grenoble (2003).
[3] Riemannian manifolds with non-negative Ricci curvature, Duke Math. J. 39 (1972) 55-64. | MR 290286 | Zbl 0251.53017
,[4] Sobolev inequalities and Myers' diameter theorem for an abstract Markov generator, Duke Math. J. (1996) 253-270. | MR 1412446 | Zbl 0870.60071
, ,[5] On Ricci curvature and geodesics, Duke Math. J. 34 (1967) 667-676. | MR 216429 | Zbl 0153.51501
,[6] Cheeger J., Degeneration of Riemannian metrics under Ricci curvature bounds, Piza (2001). | MR 2006642 | Zbl 1055.53024
[7] Manifolds with Wells of negative Curvature, Invent. Math. 103 (1991) 471-495. | MR 1091615 | Zbl 0722.53033
, ,[8] Isoperimetric inequalities based on integral norms of the Ricci curvature, Astérisque 157-158 (1988) 191-216. | Zbl 0665.53041
,[9] Metric Structures for Riemannian and Non-Riemannian Spaces, Progress in Mathematics, vol. 152, Birkhäuser, Boston, 1999. | MR 1699320 | Zbl 0953.53002
,[10] A generalization of Myers theorem and an application to relativistic cosmology, J. Diff. Geom. 14 (1979) 105-116. | MR 577883 | Zbl 0444.53036
,[11] Curvature h-principles, Ann. of Math. 142 (1995) 457-498. | MR 1356779 | Zbl 0909.58005
,[12] A Ricci curvature criterion for compactness of Riemannian manifolds, Arch. Math. 39 (1982) 85-91. | MR 674537 | Zbl 0497.53046
,[13] Riemannian manifolds with positive mean curvature, Duke Math. J. (1941) 401-404. | MR 4518 | Zbl 0025.22704
,[14] Integral curvature bounds, distance estimates and applications, J. Diff. Geom. 50 (1998) 269-298. | MR 1684981 | Zbl 0969.53017
, ,[15] Relative volume comparison with integral curvature bounds, Geom. Funct. Anal. 7 (1997) 1031-1045. | MR 1487753 | Zbl 0910.53029
, ,[16] Analysis and geometry on manifolds with integral curvature bounds. II, Trans. AMS 353 (2) (2000) 457-478. | Zbl 0999.53030
, ,[17] Bounds on the fundamental group of a manifold with almost non-negative Ricci curvature, J. Math. Soc. Japan 46 (1994) 267-287. | MR 1264942 | Zbl 0818.53058
, ,[18] Riemannian Geometry, Amer. Math. Soc., Providence, Rhode Island, 1996. | Zbl 0886.53002
,[19] Integral curvature bounds and bounded diameter, Comm. Anal. Geom. 8 (2000) 531-543. | MR 1775137 | Zbl 0984.53018
,[20] Complete manifolds with a little negative curvature, Am. J. Math. 113 (1991) 567-572. | MR 1118454 | Zbl 0744.53028
,[21] Convergence of Riemannian manifolds with integral bounds on curvature I, Ann. Sci. Éc. Norm. Sup. 25 (1992) 77-105. | Numdam | MR 1152614 | Zbl 0748.53025
,