Volume 20, issue 5 (2016)

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

Volume 27
Issue 9, 3387–3831
Issue 8, 2937–3385
Issue 7, 2497–2936
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415

Volume 26, 8 issues

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