Geometry & Topology Volume 25, issue 4 (2021)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Mixed curvature almost flat manifolds

Vitali Kapovitch

Geometry & Topology 25 (2021) 2017–2059

DOI: 10.2140/gt.2021.25.2017

Bibliography

1	S Alexander, V Kapovitch, A Petrunin, An invitation to Alexandrov geometry : CAT(0) spaces, Springer (2019) MR3930625
2	L Ambrosio, N Gigli, G Savaré, Diffusion, optimal transport and Ricci curvature for metric measure spaces, Eur. Math. Soc. Newsl. (2017) 19 MR3675945
3	D Bakry, L’hypercontractivité et son utilisation en théorie des semigroupes, from: "Lectures on probability theory" (editor P Bernard), Lecture Notes in Math. 1581, Springer (1994) 1 MR1307413
4	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
5	P Buser, D Gromoll, On the almost negatively curved 3–sphere, from: "Geometry and analysis on manifolds" (editor T Sunada), Lecture Notes in Math. 1339, Springer (1988) 78 MR961474
6	P Buser, H Karcher, Gromov’s almost flat manifolds, 81, Soc. Math. France (1981) 148 MR619537
7	A Chau, L F Tam, C Yu, Pseudolocality for the Ricci flow and applications, Canad. J. Math. 63 (2011) 55 MR2779131
8	J Cheeger, T H Colding, Lower bounds on Ricci curvature and the almost rigidity of warped products, Ann. of Math. 144 (1996) 189 MR1405949
9	J Cheeger, K Fukaya, M Gromov, Nilpotent structures and invariant metrics on collapsed manifolds, J. Amer. Math. Soc. 5 (1992) 327 MR1126118
10	J Cheeger, M Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded, I, J. Differential Geom. 23 (1986) 309 MR852159
11	J Cheeger, M Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded, II, J. Differential Geom. 32 (1990) 269 MR1064875
12	L Chen, X Rong, S Xu, Quantitative volume space form rigidity under lower Ricci curvature bound, I, J. Differential Geom. 113 (2019) 227 MR4023292
13	B Chow, S C Chu, D Glickenstein, C Guenther, J Isenberg, T Ivey, D Knopf, P Lu, F Luo, L Ni, The Ricci flow : techniques and applications, III : Geometric-analytic aspects, 163, Amer. Math. Soc. (2010) MR2604955
14	M Erbar, K Kuwada, K T Sturm, On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces, Invent. Math. 201 (2015) 993 MR3385639
15	F T Farrell, W C Hsiang, Topological characterization of flat and almost flat Riemannian manifolds Mⁿ (n≠3,4), Amer. J. Math. 105 (1983) 641 MR704219
16	F T Farrell, L E Jones, The surgery L–groups of poly-(finite or cyclic) groups, Invent. Math. 91 (1988) 559 MR928498
17	D Fisher, B Kalinin, R Spatzier, Global rigidity of higher rank Anosov actions on tori and nilmanifolds, J. Amer. Math. Soc. 26 (2013) 167 MR2983009
18	M H Freedman, The disk theorem for four-dimensional manifolds, from: "Proceedings of the International Congress of Mathematicians, I" (editors Z Ciesielski, C Olech), PWN (1984) 647 MR804721
19	K Fukaya, T Yamaguchi, The fundamental groups of almost non-negatively curved manifolds, Ann. of Math. 136 (1992) 253 MR1185120
20	N Gigli, The splitting theorem in non-smooth context, preprint (2013) arXiv:1302.5555
21	N Gigli, An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature, Anal. Geom. Metr. Spaces 2 (2014) 169 MR3210895
22	M Gromov, Almost flat manifolds, J. Differential Geom. 13 (1978) 231 MR540942
23	R S Hamilton, The formation of singularities in the Ricci flow, from: "Surveys in differential geometry, II" (editor S T Yau), International (1995) 7 MR1375255
24	H Huang, L Kong, X Rong, S Xu, Collapsed manifolds with Ricci bounded covering geometry, Trans. Amer. Math. Soc. 373 (2020) 8039 MR4169681
25	V Kapovitch, M Kell, C Ketterer, On the structure of RCD spaces with upper curvature bounds, preprint (2019) arXiv:1908.07036
26	V Kapovitch, C Ketterer, CD meets CAT, J. Reine Angew. Math. 766 (2020) 1 MR4145200
27	V Kapovitch, A Petrunin, W Tuschmann, Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces, Ann. of Math. 171 (2010) 343 MR2630041
28	V Kapovitch, B Wilking, Structure of fundamental groups of manifolds with Ricci curvature bounded below, preprint (2011) arXiv:1105.5955
29	Y Kitabeppu, A sufficient condition to a regular set being of positive measure on RCD spaces, Potential Anal. 51 (2019) 179 MR3983504
30	B Kleiner, J Lott, Notes on Perelman’s papers, Geom. Topol. 12 (2008) 2587 MR2460872
31	K B Lee, F Raymond, Rigidity of almost crystallographic groups, from: "Combinatorial methods in topology and algebraic geometry" (editors J R Harper, R Mandelbaum), Contemp. Math. 44, Amer. Math. Soc. (1985) 73 MR813102
32	J Lott, Some geometric properties of the Bakry–Émery–Ricci tensor, Comment. Math. Helv. 78 (2003) 865 MR2016700
33	J Lott, Optimal transport and Perelman’s reduced volume, Calc. Var. Partial Differential Equations 36 (2009) 49 MR2507614
34	J Lott, Dimensional reduction and the long-time behavior of Ricci flow, Comment. Math. Helv. 85 (2010) 485 MR2653690
35	J Lott, C Villani, Ricci curvature for metric-measure spaces via optimal transport, Ann. of Math. 169 (2009) 903 MR2480619
36	B O’Neill, Semi-Riemannian geometry : with applications to relativity, 103, Academic (1983) MR719023
37	E K Pedersen, The surgery exact sequence revisited, from: "High-dimensional manifold topology" (editors F T Farrell, W Lück), World Sci. (2003) 416 MR2048730
38	G Perelman, The entropy formula for the Ricci flow and its geometric applications, preprint (2002) arXiv:math/0211159
39	X Rong, Collapsed manifolds with bounded sectional curvature and applications, from: "Surveys in differential geometry, XI" (editors J Cheeger, K Grove), International (2007) 1 MR2408262
40	E A Ruh, Almost flat manifolds, J. Differential Geom. 17 (1982) 1 MR658470
41	C Villani, Synthetic theory of Ricci curvature bounds, Jpn. J. Math. 11 (2016) 219 MR3544918
42	T Yamaguchi, Collapsing and pinching under a lower curvature bound, Ann. of Math. 133 (1991) 317 MR1097241