Le théorème de la sphère différentiable [d'après Brendle-Schoen]

Besson, Gérard

Séminaire Bourbaki : volume 2008/2009 exposés 997-1011 - Avec table par noms d'auteurs de 1848/49 à 2008/09, Astérisque, no. 332 (2010), Exposé no. 1003, 21 p.

MR Zbl

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     author = {Besson,  G\'erard},
     title = {Le th\'eor\`eme de la sph\`ere diff\'erentiable [d'apr\`es {Brendle-Schoen]}},
     booktitle = {S\'eminaire Bourbaki : volume 2008/2009 expos\'es 997-1011  - Avec table par noms d'auteurs de 1848/49 \`a 2008/09},
     series = {Ast\'erisque},
     note = {talk:1003},
     pages = {161--181},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {332},
     year = {2010},
     mrnumber = {2648678},
     zbl = {1220.53043},
     language = {fr},
     url = {http://archive.numdam.org/item/AST_2010__332__161_0/}
}

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Besson,  Gérard. Le théorème de la sphère différentiable [d'après Brendle-Schoen], dans Séminaire Bourbaki : volume 2008/2009 exposés 997-1011  - Avec table par noms d'auteurs de 1848/49 à 2008/09, Astérisque, no. 332 (2010), Exposé no. 1003, 21 p. http://archive.numdam.org/item/AST_2010__332__161_0/

Bibliographie
Cité par

[1] M. Berger - Les variétés Riemanniennes $(1 / 4)$ -pincées, Ann. Scuola Norm. Sup. Pisa 14 (1960), p. 161-170. | EuDML | Numdam | MR | Zbl

[2] M. Berger, Sur quelques variétés riemanniennes suffisamment pincées, Bull. Soc. Math. France 88 (1960), p. 57-71. | DOI | EuDML | Numdam | MR | Zbl

[3] M. Berger, Sur les variétés riemanniennes pincées juste au-dessous de 1/4, Ann. Inst. Fourier (Grenoble) 33 (1983), p. 135-150. | DOI | EuDML | Numdam | MR | Zbl

[4] M. Berger, A panoramic view of Riemannian geometry, Springer, 2003. | DOI | MR | Zbl

[5] G. Besson - Preuve de la conjecture de Poincaré en déformant la métrique par la courbure de Ricci (d'après G. Perel'man), Séminaire Bourbaki, vol. 2004/2005, exposé n° 947, Astérisque 307 (2006), p. 309-347. | EuDML | Numdam | MR | Zbl

[6] C. Böhm & B. Wilking - Manifolds with positive curvature operators are space forms, Ann. of Math. 167 (2008), p. 1079-1097. | DOI | MR | Zbl

[7] S. Brendle - Einstein manifolds with nonnegative isotropic curvature are locally symmetric, prépublication arXiv:0812.0335, 2008. | MR | Zbl

[8] S. Brendle, A general convergence result for the Ricci flow in higher dimensions, Duke Math. J. 145 (2008), p. 585-601. | DOI | MR | Zbl

[9] S. Brendle, Ricci flow and the sphere theorem, Graduate Studies in Math., vol. 111, Amer. Math. Soc., 2010. | DOI | MR | Zbl

[10] S. Brendle & R. M. Schoen - Classification of manifolds with weakly $1 / 4$ -pinched curvatures, Acta Math. 200 (2008), p. 1-13. | DOI | MR | Zbl

[11] S. Brendle & R. M. Schoen, Manifolds with $1 / 4$ -pinched curvature are space forms, J. Amer. Math. Soc. 22 (2009), p. 287-307. | DOI | MR | Zbl

[12] S. Brendle & R. M. Schoen, Sphere theorems in geometry, in Surveys in differential geometry. Vol. XIII. Geometry, analysis, and algebraic geometry : forty years of the Journal of Differential Geometry, Surv. Differ. Geom., vol. 13, Int. Press, Somerville, MA, 2009, p. 49-84. | DOI | MR | Zbl

[13] B.-L. Chen & X.-P. Zhu - Ricci flow with surgery on four-manifolds with positive isotropic curvature, J. Differential Geom. 74 (2006), p. 177-264. | DOI | MR | Zbl

[14] H. Chen - Pointwise $\frac{1}{4}$ -pinched $4$ -manifolds, Ann. Global Anal. Geom. 9 (1991), p. 161-176. | DOI | MR | Zbl

[15] B. Chow et al. - The Ricci flow : techniques and applications. Part I, Math. Surveys and Monographs, vol. 135, Amer. Math. Soc., 2007. | MR | Zbl

[16] B. Chow et al., The Ricci flow : techniques and applications. Part II, Math. Surveys and Monographs, vol. 144, Amer. Math. Soc., 2008. | DOI | MR | Zbl

[17] B. Chow & D. Knopf - The Ricci flow : an introduction, Math. Surveys and Monographs, vol. 110, Amer. Math. Soc., 2004. | DOI | MR | Zbl

[18] A. M. Fraser - Fundamental groups of manifolds with positive isotropic curvature, Ann. of Math. 158 (2003), p. 345-354. | DOI | MR | Zbl

[19] A. M. Fraser & J. Wolfson - The fundamental group of manifolds of positive isotropic curvature and surface groups, Duke Math. J. 133 (2006), p. 325-334. | DOI | MR | Zbl

[20] S. Gadgil & H. Seshadri - On the topology of manifolds with positive isotropic curvature, Proc. Amer. Math. Soc. 137 (2009), p. 1807-1811. | DOI | MR | Zbl

[21] S. Gallot, D. Hulin & J. Lafontaine - Riemannian geometry, 3e ed., Universitext, Springer, 2004. | MR

[22] R. S. Hamilton - Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), p. 255-306. | DOI | MR | Zbl

[23] R. S. Hamilton, Four-manifolds with positive curvature operator, J. Differential Geom. 24 (1986), p. 153-179. | DOI | MR | Zbl

[24] R. S. Hamilton, A compactness property for solutions of the Ricci flow, Amer. J. Math. 117 (1995), p. 545-572. | DOI | MR | Zbl

[25] R. S. Hamilton, The formation of singularities in the Ricci flow, in Surveys in differential geometry, Vol. II (Cambridge, MA, 1993), Int. Press, Cambridge, MA, 1995, p. 7-136. | MR | Zbl

[26] R. S. Hamilton, Four-manifolds with positive isotropic curvature, Comm. Anal. Geom. 5 (1997), p. 1-92. | DOI | MR | Zbl

[27] L. Hernandez - Kähler manifolds and $1 / 4$ -pinching, Duke Math. J. 62 (1991), p. 601-611. | DOI | MR | Zbl

[28] G. Huisken - Ricci deformation of the metric on a Riemannian manifold, J. Differential Geom. 21 (1985), p. 47-62. | DOI | MR | Zbl

[29] W. Klingenberg - Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung, Comment. Math. Helv. 35 (1961), p. 47-54. | DOI | EuDML | MR | Zbl

[30] C. Margerin - A sharp characterization of the smooth $4$ -sphere in curvature terms, Comm. Anal. Geom. 6 (1998), p. 21-65. | DOI | MR | Zbl

[31] M. J. Micallef & J. D. Moore - Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes, Ann. of Math. 127 (1988), p. 199-227. | DOI | MR | Zbl

[32] M. J. Micallef & M. Y. Wang - Metrics with nonnegative isotropic curvature, Duke Math. J. 72 (1993), p. 649-672. | DOI | MR | Zbl

[33] H. Nguyen - Isotropic curvature and the Ricci flow, prépublication, 2007. | Zbl

[34] S. Nishikawa - Deformation of Riemannian metrics and manifolds with bounded curvature ratios, in Geometric measure theory and the calculus of variations (Areata, Calif., 1984), Proc. Sympos. Pure Math., vol. 44, Amer. Math. Soc., 1986, p. 343-352. | DOI | MR | Zbl

[35] G. Perelman - The entropy formula for the Ricci flow and its geometric applications, prépublication arXiv:math.DG/0211159, 2002. | Zbl

[36] G. Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, prépublication arXiv:math.DG/0307245, 2003. | Zbl

[37] G. Perelman, Ricci flow with surgery on three-manifolds, prépublication arXiv:math.DG/0303109, 2003. | Zbl

[38] P. Petersen & T. Tao - Classification of almost quarter-pinched manifolds, Proc. Amer. Math. Soc. 137 (2009), p. 2437-2440. | DOI | MR | Zbl

[39] P. Petersen & F. Wilhelm - An exotic sphere with positive sectional curvature, prépublication arXiv:0805.0812, 2008.

[40] H. E. Rauch - A contribution to differential geometry in the large, Ann. of Math. 54 (1951), p. 38-55. | DOI | MR | Zbl

[41] H. Seshadri - Manifolds with nonnegative isotropic curvature, prépublication arXiv:0707.3894, 2008. | MR | Zbl

[42] A. Besse - Einstein manifolds, Ergebnisse Math. Grenzg. (3), vol. 10, Springer, 1987. | MR | Zbl

[43] S.-T. Yau & F. Zheng - Negatively $\frac{1}{4}$ -pinched Riemannian metric on a compact Kähler manifold, Invent. Math. 103 (1991), p. 527-535. | DOI | EuDML | MR | Zbl