Volume 20, issue 5 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Topology and $\epsilon$–regularity theorems on collapsed manifolds with Ricci curvature bounds

Aaron Naber and Ruobing Zhang

Geometry & Topology 20 (2016) 2575–2664
Bibliography
1 M T Anderson, Convergence and rigidity of manifolds under Ricci curvature bounds, Invent. Math. 102 (1990) 429 MR1074481
2 M T Anderson, Hausdorff perturbations of Ricci-flat manifolds and the splitting theorem, Duke Math. J. 68 (1992) 67 MR1185818
3 M T Anderson, The L2 structure of moduli spaces of Einstein metrics on 4–manifolds, Geom. Funct. Anal. 2 (1992) 29 MR1143663
4 J Cheeger, T H Colding, Lower bounds on Ricci curvature and the almost rigidity of warped products, Ann. of Math. 144 (1996) 189 MR1405949
5 J Cheeger, T H Colding, On the structure of spaces with Ricci curvature bounded below, I, J. Differential Geom. 46 (1997) 406 MR1484888
6 J Cheeger, D Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geometry 6 (1971/72) 119 MR0303460
7 J Cheeger, A Naber, Lower bounds on Ricci curvature and quantitative behavior of singular sets, Invent. Math. 191 (2013) 321 MR3010378
8 J Cheeger, A Naber, Regularity of Einstein manifolds and the codimension 4 conjecture, Ann. of Math. 182 (2015) 1093 MR3418535
9 J Cheeger, G Tian, Curvature and injectivity radius estimates for Einstein 4–manifolds, J. Amer. Math. Soc. 19 (2006) 487 MR2188134
10 S Y Cheng, S T Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975) 333 MR0385749
11 T H Colding, A Naber, Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications, Ann. of Math. 176 (2012) 1173 MR2950772
12 X Dai, G Wei, R Ye, Smoothing Riemannian metrics with Ricci curvature bounds, Manuscripta Math. 90 (1996) 49 MR1387754
13 K Fukaya, T Yamaguchi, The fundamental groups of almost nonnegatively curved manifolds, Ann. of Math. 136 (1992) 253 MR1185120
14 M Gromov, Almost flat manifolds, J. Differential Geom. 13 (1978) 231 MR540942
15 M Gross, V Tosatti, Y Zhang, Gromov–Hausdorff collapsing of Calabi–Yau manifolds, arXiv:1304.1820
16 M Gross, P M H Wilson, Large complex structure limits of K3 surfaces, J. Differential Geom. 55 (2000) 475 MR1863732
17 V Kapovitch, A Petrunin, W Tuschmann, Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces, Ann. of Math. 171 (2010) 343 MR2630041
18 V Kapovitch, B Wilking, Structure of fundamental groups of manifolds with Ricci curvature bounded below, arXiv:1105.5955
19 M I Kargapolov, J I Merzljakov, Fundamentals of the theory of groups, 62, Springer (1979) MR551207
20 M S Raghunathan, Discrete subgroups of Lie groups, 68, Springer (1972) MR0507234
21 E A Ruh, Almost flat manifolds, J. Differential Geom. 17 (1982) 1 MR658470
22 Á Seress, Permutation group algorithms, 152, Cambridge Univ. Press (2003) MR1970241
23 G Wei, Examples of complete manifolds of positive Ricci curvature with nilpotent isometry groups, Bull. Amer. Math. Soc. 19 (1988) 311 MR940494
24 T Yamaguchi, Collapsing and pinching under a lower curvature bound, Ann. of Math. 133 (1991) 317 MR1097241
25 T Yamaguchi, A convergence theorem in the geometry of Alexandrov spaces, from: "Actes de la Table Ronde de Géométrie Différentielle" (editor A L Besse), Sémin. Congr. 1, Soc. Math. France (1996) 601 MR1427772