@incollection{AST_2014__365__7_0, author = {Kleiner, Bruce and Lott, John}, title = {Locally collapsed $3$-manifolds}, booktitle = {Local collapsing, orbifolds, and geometrization}, series = {Ast\'erisque}, pages = {7--99}, publisher = {Soci\'et\'e math\'ematique de France}, number = {365}, year = {2014}, mrnumber = {3244329}, language = {en}, url = {http://www.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 - Collectif T3 - Astérisque PY - 2014 SP - 7 EP - 99 IS - 365 PB - Société mathématique de France UR - http://www.numdam.org/item/AST_2014__365__7_0/ 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), pp. 7-99. http://www.numdam.org/item/AST_2014__365__7_0/
[1] The structure of moduli spaces of Einstein metrics on -manifolds", Geom. Funct. Anal. 2 (1992), no. 1, p. 29-89. | DOI | EuDML | MR | Zbl
- "[2] Collapsing irreducible -manifolds with nontrivial fundamental group", Invent. Math. 179 (2010), no. 2, p. 435-460. | DOI | MR | Zbl
, , , & - "[3] A course in metric geometry, Grad. Stud. Math., vol. 33, Amer. Math. Soc., Providence, RI, 2001. | DOI | MR | Zbl
, & -[4] A. D. Aleksandrov spaces with curvatures bounded below", Uspekhi Mat. Nauk 47 (1992), no. 2(284), p. 3-51, 222. | MR | Zbl
, & - "[5] A simple proof of Perelman's collapsing theorem for -manifolds", J. Geom. Anal. 21 (2011), no. 4, p. 807-869. | DOI | MR | Zbl
& - "[6] 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 | Zbl
- "[7] On the structure of complete manifolds of nonnegative curvature", Ann. of Math. (2) 96 (1972), p. 413-443. | DOI | MR | Zbl
& - "[8] Collapsing Riemannian manifolds while keeping their curvature bounded. I", J. Differential Geom. 23 (1986), no. 3, p. 309-346. | DOI | MR | Zbl
& - "[9] Collapsing Riemannian manifolds while keeping their curvature bounded. II", J. Differential Geom. 32 (1990), no. 1, p. 269-298. | DOI | MR | Zbl
& , "[10] Curvature and injectivity radius estimates for Einstein -manifolds", J. Amer. Math. Soc. 19 (2006), no. 2, p. 487-525 (electronic). | DOI | MR | Zbl
& - "[11] Optimization and nonsmooth analysis, second ed., Classics Appl. Math., vol. 5, Soc. Ind. Appl. Math. (SIAM), Philadelphia, PA, 1990. | MR | Zbl
-[12] Collapsing Riemannian manifolds to ones of lower dimensions", J. Differential Geom. 25 (1987), no. 1, p. 139-156. | DOI | MR | Zbl
- "[13] Almost flat manifolds", J. Differential Geom. 13 (1978), no. 2, p. 231-241. | DOI | MR | Zbl
- "[14] Metric structures for Riemannian and non-Riemannian spaces, Progr. Math., vol. 152, Birkhäuser Boston, Inc., Boston, MA, 1999. | MR | Zbl
,[15] Bounding homotopy types by geometry", Ann. of Math. (2) 128 (1988), no. 1, p. 195-206. | DOI | MR | Zbl
& , V - "[16] A generalized sphere theorem", Ann. of Math. (2) 106 (1977), no. 2, p. 201-211. | DOI | MR | Zbl
& - "[17] Three-manifolds with positive Ricci curvature", J. Differential Geom. 17 (1982), no. 2, p. 255-306. | DOI | MR | Zbl
- "[18] Four-manifolds with positive curvature operator", J. Differential Geom. 24 (1986), no. 2, p. 153-179. | DOI | MR | Zbl
, "[19] Perelman's stability theorem", in Surveys in differential geometry. Vol. XI, Surv. Differ. Geom., vol. 11, Int. Press, Somerville, MA, 2007, p. 103-136. | DOI | MR | Zbl
- "[20] Gromov's convergence theorem and its application", Nagoya Math. J. 100 (1985), p. 11-48. | DOI | MR | Zbl
"[21] Notes on Perelman's papers", Geom. Topol. 12 (2008), no. 5, p. 2587-2855. | DOI | MR | Zbl
& "[22] Algorithmic topology and classification of -manifolds, Algorithms Comput. Math., vol. 9, Springer-Verlag, Berlin, 2003. | DOI | MR | Zbl
-[23] The geometrization conjecture, Clay Math. Monogr., vol. 5, Amer. Math. Soc./Clay Math. Inst., Providence, RI/Cambridge, MA, 2014. | MR | Zbl
& -[24] Ricci Flow with Surgery on Three-Manifolds", http://arxiv.org/abs/math.DG/0303109. | Zbl
- "[25] Alexandrov's Spaces with Curvature Bounded from Below II", preprint, 1991. | Zbl
, "[26] Riemannian geometry, second ed., Grad. Texts in Math., vol. 171, Springer, New York, 2006. | DOI | MR | Zbl
-[27] Smoothing a topological manifold", Topology Appl. 124 (2002), no. 3, p. 487-503. | DOI | MR | Zbl
- "[28] Solution of the Plateau Problem for -dimensional surfaces of varying topological type", Acta Math. 104 (1960) , p. 1-92. | DOI | MR | Zbl
- "[29] Collapsing three-manifolds under a lower curvature bound", J. Differential Geom. 56 (2000), no. 1, p. 1-66. | DOI | MR | Zbl
& - "[30] Volume collapsed three-manifolds with a lower curvature bound", Math. Ann. 333 (2005), no. 1, p. 131-155. | DOI | MR | Zbl
& ,"[31] Ricci flow of almost non-negatively curved three manifolds", J. Reine Angew. Math. 630 (2009), p. 177-217. | MR | Zbl
- "[32] On fibering certain -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 | Zbl
"[33] Collapsing and pinching under a lower curvature bound", Ann. of Math. (2) 133 (1991) , no. 2, p. 317-357. | DOI | MR | Zbl
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