Finiteness of π 1 and geometric inequalities in almost positive Ricci curvature
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 40 (2007) no. 4, pp. 675-695.
@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},
     pages = {675--695},
     publisher = {Elsevier},
     volume = {Ser. 4, 40},
     number = {4},
     year = {2007},
     doi = {10.1016/j.ansens.2007.07.001},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.ansens.2007.07.001/}
}
TY  - JOUR
AU  - Aubry, Erwann
TI  - Finiteness of ${\pi }_{1}$ and geometric inequalities in almost positive Ricci curvature
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2007
DA  - 2007///
SP  - 675
EP  - 695
VL  - Ser. 4, 40
IS  - 4
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.ansens.2007.07.001/
UR  - https://doi.org/10.1016/j.ansens.2007.07.001
DO  - 10.1016/j.ansens.2007.07.001
LA  - en
ID  - ASENS_2007_4_40_4_675_0
ER  - 
%0 Journal Article
%A Aubry, Erwann
%T Finiteness of ${\pi }_{1}$ and geometric inequalities in almost positive Ricci curvature
%J Annales scientifiques de l'École Normale Supérieure
%D 2007
%P 675-695
%V Ser. 4, 40
%N 4
%I Elsevier
%U https://doi.org/10.1016/j.ansens.2007.07.001
%R 10.1016/j.ansens.2007.07.001
%G en
%F 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, Serie 4, Volume 40 (2007) no. 4, pp. 675-695. doi : 10.1016/j.ansens.2007.07.001. http://archive.numdam.org/articles/10.1016/j.ansens.2007.07.001/

[1] Ambrose W., A theorem of Myers, Duke Math. J. 24 (1957) 345-348. | MR | Zbl

[2] Aubry E., Variétés de courbure de Ricci presque minorée : inégalités géométriques optimales et stabilité des variétés extrémales, Thèse, Institut Fourier, Grenoble (2003).

[3] Avez A., Riemannian manifolds with non-negative Ricci curvature, Duke Math. J. 39 (1972) 55-64. | MR | Zbl

[4] Bakry D., Ledoux M., Sobolev inequalities and Myers' diameter theorem for an abstract Markov generator, Duke Math. J. (1996) 253-270. | MR | Zbl

[5] Calabi E., On Ricci curvature and geodesics, Duke Math. J. 34 (1967) 667-676. | MR | Zbl

[6] Cheeger J., Degeneration of Riemannian metrics under Ricci curvature bounds, Piza (2001). | MR | Zbl

[7] Elworthy K., Rosenberg S., Manifolds with Wells of negative Curvature, Invent. Math. 103 (1991) 471-495. | MR | Zbl

[8] Gallot S., Isoperimetric inequalities based on integral norms of the Ricci curvature, Astérisque 157-158 (1988) 191-216. | Zbl

[9] Gromov M., Metric Structures for Riemannian and Non-Riemannian Spaces, Progress in Mathematics, vol. 152, Birkhäuser, Boston, 1999. | MR | Zbl

[10] Galloway G., A generalization of Myers theorem and an application to relativistic cosmology, J. Diff. Geom. 14 (1979) 105-116. | MR | Zbl

[11] Lohkamp J., Curvature h-principles, Ann. of Math. 142 (1995) 457-498. | MR | Zbl

[12] Markvorsen S., A Ricci curvature criterion for compactness of Riemannian manifolds, Arch. Math. 39 (1982) 85-91. | MR | Zbl

[13] Myers S., Riemannian manifolds with positive mean curvature, Duke Math. J. (1941) 401-404. | MR | Zbl

[14] Petersen P., Sprouse C., Integral curvature bounds, distance estimates and applications, J. Diff. Geom. 50 (1998) 269-298. | MR | Zbl

[15] Petersen P., Wei G., Relative volume comparison with integral curvature bounds, Geom. Funct. Anal. 7 (1997) 1031-1045. | MR | Zbl

[16] Petersen P., Wei G., Analysis and geometry on manifolds with integral curvature bounds. II, Trans. AMS 353 (2) (2000) 457-478. | Zbl

[17] Rosenberg S., Yang D., Bounds on the fundamental group of a manifold with almost non-negative Ricci curvature, J. Math. Soc. Japan 46 (1994) 267-287. | MR | Zbl

[18] Sakai T., Riemannian Geometry, Amer. Math. Soc., Providence, Rhode Island, 1996. | Zbl

[19] Sprouse C., Integral curvature bounds and bounded diameter, Comm. Anal. Geom. 8 (2000) 531-543. | MR | Zbl

[20] Wu J., Complete manifolds with a little negative curvature, Am. J. Math. 113 (1991) 567-572. | MR | Zbl

[21] Yang D., Convergence of Riemannian manifolds with integral bounds on curvature I, Ann. Sci. Éc. Norm. Sup. 25 (1992) 77-105. | Numdam | MR | Zbl

Cited by Sources: