Locally collapsed 3-manifolds
Local collapsing, orbifolds, and geometrization, Astérisque, no. 365 (2014), 93 p.
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez le site de la revue.
@inbook{AST_2014__365__7_0,
     author = {Kleiner, Bruce and Lott, John},
     title = {Locally collapsed $3$-manifolds},
     booktitle = {Local collapsing, orbifolds, and geometrization},
     author = {Kleiner, Bruce and Lott, John},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {365},
     year = {2014},
     mrnumber = {3244329},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2014__365__7_0/}
}
TY  - CHAP
AU  - Kleiner, Bruce
AU  - Lott, John
TI  - Locally collapsed $3$-manifolds
BT  - Local collapsing, orbifolds, and geometrization
AU  - Kleiner, Bruce
AU  - Lott, John
T3  - Astérisque
PY  - 2014
DA  - 2014///
IS  - 365
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_2014__365__7_0/
UR  - https://www.ams.org/mathscinet-getitem?mr=3244329
LA  - en
ID  - AST_2014__365__7_0
ER  - 
Kleiner, Bruce; Lott, John. Locally collapsed $3$-manifolds, dans Local collapsing, orbifolds, and geometrization, Astérisque, no. 365 (2014), 93 p. http://archive.numdam.org/item/AST_2014__365__7_0/

[1] M. T. Anderson - "The L 2 structure of moduli spaces of Einstein metrics on 4-manifolds", Geom. Funct. Anal. 2 (1992), no. 1, p. 29-89. | Article | EuDML 58134 | MR 1143663 | Zbl 0768.53021

[2] L. Bessières, G. Besson, M. Boileau, S. Maillot& J. Porti - "Collapsing irreducible 3-manifolds with nontrivial fundamental group", Invent. Math. 179 (2010), no. 2, p. 435-460. | Article | MR 2570121 | Zbl 1188.57013

[3] D. Burago, Y. Burago & S. Ivanov - A course in metric geometry, Grad. Stud. Math., vol. 33, Amer. Math. Soc., Providence, RI, 2001. | Article | MR 1835418 | Zbl 0981.51016

[4] Y. Burago, M. Gromov & G. Perel'Man - "A. D. Aleksandrov spaces with curvatures bounded below", Uspekhi Mat. Nauk 47 (1992), no. 2(284), p. 3-51, 222. | MR 1185284 | Zbl 0802.53018

[5] J. Cao & J. Ge - "A simple proof of Perelman's collapsing theorem for 3-manifolds", J. Geom. Anal. 21 (2011), no. 4, p. 807-869. | Article | MR 2836584 | Zbl 1246.53052

[6] J. Cheeger - "Critical points of distance functions and applications to geometry", in Geometric topology: recent developments (Montecatini Terme, 1990), Lecture Notes in Math., vol. 1504, Springer, Berlin, 1991, p. 1-38. | MR 1168042 | Zbl 0771.53015

[7] J. Cheeger & D. Gromoll - "On the structure of complete manifolds of nonnegative curvature", Ann. of Math. (2) 96 (1972), p. 413-443. | Article | MR 309010 | Zbl 0246.53049

[8] J. Cheeger & M. Gromov - "Collapsing Riemannian manifolds while keeping their curvature bounded. I", J. Differential Geom. 23 (1986), no. 3, p. 309-346. | Article | MR 852159 | Zbl 0606.53028

[9] J. Cheeger & M. Gromov, "Collapsing Riemannian manifolds while keeping their curvature bounded. II", J. Differential Geom. 32 (1990), no. 1, p. 269-298. | Article | MR 1064875 | Zbl 0727.53043

[10] J. Cheeger & G. Tian - "Curvature and injectivity radius estimates for Einstein 4-manifolds", J. Amer. Math. Soc. 19 (2006), no. 2, p. 487-525 (electronic). | Article | MR 2188134 | Zbl 1092.53034

[11] F. H. Clarke - Optimization and nonsmooth analysis, second ed., Classics Appl. Math., vol. 5, Soc. Ind. Appl. Math. (SIAM), Philadelphia, PA, 1990. | MR 1058436 | Zbl 0696.49002

[12] K. Fukaya - "Collapsing Riemannian manifolds to ones of lower dimensions", J. Differential Geom. 25 (1987), no. 1, p. 139-156. | Article | MR 873459 | Zbl 0606.53027

[13] M. Gromov - "Almost flat manifolds", J. Differential Geom. 13 (1978), no. 2, p. 231-241. | Article | MR 540942 | Zbl 0432.53020

[14] M. Gromov, Metric structures for Riemannian and non-Riemannian spaces, Progr. Math., vol. 152, Birkhäuser Boston, Inc., Boston, MA, 1999. | MR 1699320 | Zbl 0953.53002

[15] K. Grove & P. Petersen, V - "Bounding homotopy types by geometry", Ann. of Math. (2) 128 (1988), no. 1, p. 195-206. | Article | MR 951512 | Zbl 0655.53032

[16] K. Grove & K. Shiohama - "A generalized sphere theorem", Ann. of Math. (2) 106 (1977), no. 2, p. 201-211. | Article | MR 500705 | Zbl 0341.53029

[17] R. S. Hamilton - "Three-manifolds with positive Ricci curvature", J. Differential Geom. 17 (1982), no. 2, p. 255-306. | Article | MR 664497 | Zbl 0504.53034

[18] R. S. Hamilton, "Four-manifolds with positive curvature operator", J. Differential Geom. 24 (1986), no. 2, p. 153-179. | Article | MR 862046 | Zbl 0628.53042

[19] V. Kapovitch - "Perelman's stability theorem", in Surveys in differential geometry. Vol. XI, Surv. Differ. Geom., vol. 11, Int. Press, Somerville, MA, 2007, p. 103-136. | Article | MR 2408265 | Zbl 1151.53038

[20] A. Katsuda "Gromov's convergence theorem and its application", Nagoya Math. J. 100 (1985), p. 11-48. | Article | MR 818156 | Zbl 0587.53043

[21] B. Kleiner & J. Lott "Notes on Perelman's papers", Geom. Topol. 12 (2008), no. 5, p. 2587-2855. | Article | MR 2460872 | Zbl 1204.53033

[22] S. Matveev - Algorithmic topology and classification of 3-manifolds, Algorithms Comput. Math., vol. 9, Springer-Verlag, Berlin, 2003. | Article | MR 1997069 | Zbl 1048.57001

[23] J. Morgan & G. Tian - The geometrization conjecture, Clay Math. Monogr., vol. 5, Amer. Math. Soc./Clay Math. Inst., Providence, RI/Cambridge, MA, 2014. | MR 3186136 | Zbl 1302.53001

[24] G. Perelman - "Ricci Flow with Surgery on Three-Manifolds", http://arxiv.org/abs/math.DG/0303109. | Zbl 1130.53002

[25] G. Perelman, "Alexandrov's Spaces with Curvature Bounded from Below II", preprint, 1991. | Zbl 0802.53018

[26] P. Petersen - Riemannian geometry, second ed., Grad. Texts in Math., vol. 171, Springer, New York, 2006. | Article | MR 2243772 | Zbl 1220.53002

[27] C. C. Pugh - "Smoothing a topological manifold", Topology Appl. 124 (2002), no. 3, p. 487-503. | Article | MR 1930659 | Zbl 1026.57019

[28] E. R. Reifenberg - "Solution of the Plateau Problem for m-dimensional surfaces of varying topological type", Acta Math. 104 (1960) , p. 1-92. | Article | MR 114145 | Zbl 0099.08503

[29] T. Shioya & T. Yamaguchi - "Collapsing three-manifolds under a lower curvature bound", J. Differential Geom. 56 (2000), no. 1, p. 1-66. | Article | MR 1863020 | Zbl 1036.53028

[30] T. Shioya & T. Yamaguchi,"Volume collapsed three-manifolds with a lower curvature bound", Math. Ann. 333 (2005), no. 1, p. 131-155. | Article | MR 2169831 | Zbl 1087.53033

[31] M. Simon - "Ricci flow of almost non-negatively curved three manifolds", J. Reine Angew. Math. 630 (2009), p. 177-217. | MR 2526789 | Zbl 1165.53046

[32] J. Stallings "On fibering certain 3-manifolds", in Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961), Prentice-Hall, Englewood Cliffs, N.J. 1962, p. 95-100. | MR 158375 | Zbl 1246.57049

[33] T. Yamaguchi - "Collapsing and pinching under a lower curvature bound", Ann. of Math. (2) 133 (1991) , no. 2, p. 317-357. | Article | MR 1097241 | Zbl 0737.53041