Volume 22, issue 2 (2018)

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

Volume 23
Issue 2, 541–1084
Issue 1, 1–540

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
Long-time behavior of $3$–dimensional Ricci flow, D: Proof of the main results

Richard H Bamler

Geometry & Topology 22 (2018) 949–1068
Bibliography
1 R Bamler, Long-time behavior of 3–dimensional Ricci flow : introduction, Geom. Topol. 22 (2018)
2 R Bamler, Long-time behavior of 3–dimensional Ricci flow, A : Generalizations of Perelman’s long-time estimates, Geom. Topol. 22 (2018)
3 R Bamler, Long-time behavior of 3–dimensional Ricci flow, B : Evolution of the minimal area of simplicial complexes under Ricci flow, Geom. Topol. 22 (2018)
4 R Bamler, Long-time behavior of 3–dimensional Ricci flow, C : 3–manifold topology and combinatorics of simplicial complexes in 3–manifolds, Geom. Topol. 22 (2018)
5 R H Bamler, Stability of hyperbolic manifolds with cusps under Ricci flow, Adv. Math. 263 (2014) 412 MR3239144
6 R H Bamler, The long-time behavior of 3–dimensional Ricci flow on certain topologies, J. Reine Angew. Math. 725 (2017) 183 MR3630121
7 L Bessières, G Besson, M Boileau, S Maillot, J Porti, Collapsing irreducible 3–manifolds with nontrivial fundamental group, Invent. Math. 179 (2010) 435 MR2570121
8 D Burago, Y Burago, S Ivanov, A course in metric geometry, 33, Amer. Math. Soc. (2001) MR1835418
9 Y Burago, M Gromov, G Perel’man, A D Aleksandrov spaces with curvatures bounded below, Uspekhi Mat. Nauk 47 (1992) 3 MR1185284
10 J Cao, J Ge, A simple proof of Perelman’s collapsing theorem for 3–manifolds, J. Geom. Anal. 21 (2011) 807 MR2836584
11 J Cheeger, K Fukaya, M Gromov, Nilpotent structures and invariant metrics on collapsed manifolds, J. Amer. Math. Soc. 5 (1992) 327 MR1126118
12 T H Colding, W P Minicozzi II, Width and finite extinction time of Ricci flow, Geom. Topol. 12 (2008) 2537 MR2460871
13 D Faessler, On the topology of locally volume collapsed Riemannian 3–orbifolds, preprint (2011) arXiv:1101.3644
14 K Fukaya, T Yamaguchi, The fundamental groups of almost non-negatively curved manifolds, Ann. of Math. 136 (1992) 253 MR1185120
15 K Grove, K Shiohama, A generalized sphere theorem, Ann. of Math. 106 (1977) 201 MR0500705
16 C Guenther, J Isenberg, D Knopf, Stability of the Ricci flow at Ricci-flat metrics, Comm. Anal. Geom. 10 (2002) 741 MR1925501
17 R D Gulliver II, Regularity of minimizing surfaces of prescribed mean curvature, Ann. of Math. 97 (1973) 275 MR0317188
18 A Hatcher, Notes on basic 3–manifold topology, book project (2007)
19 B Kleiner, J Lott, Locally collapsed 3–manifolds, from: "Local collapsing, orbifolds, and geometrization", Astérisque 365, Soc. Math. France (2014) 7 MR3244329
20 H Koch, T Lamm, Geometric flows with rough initial data, Asian J. Math. 16 (2012) 209 MR2916362
21 J Lott, Dimensional reduction and the long-time behavior of Ricci flow, Comment. Math. Helv. 85 (2010) 485 MR2653690
22 W Meyer, Toponogov’s theorem and applications, lecture notes (1989)
23 J Morgan, G Tian, Ricci flow and the Poincaré conjecture, 3, Amer. Math. Soc. (2007) MR2334563
24 J Morgan, G Tian, Completion of the proof of the geometrization conjecture, preprint (2008) arXiv:0809.4040
25 A Naber, G Tian, Geometric structures of collapsing Riemannian manifolds, I, from: "Surveys in geometric analysis and relativity" (editor H L Bray), Adv. Lect. Math. 20, International Press (2011) 439 MR2906936
26 G Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, preprint (2003) arXiv:math/0307245
27 G Perelman, Ricci flow with surgery on three-manifolds, preprint (2003) arXiv:math/0303109
28 P Petersen, Riemannian geometry, 171, Springer (2006) MR2243772
29 O C Schnürer, F Schulze, M Simon, Stability of Euclidean space under Ricci flow, Comm. Anal. Geom. 16 (2008) 127 MR2411470
30 R Schoen, Estimates for stable minimal surfaces in three-dimensional manifolds, from: "Seminar on minimal submanifolds" (editor E Bombieri), Ann. of Math. Stud. 103, Princeton Univ. Press (1983) 111 MR795231
31 T Shioya, T Yamaguchi, Volume collapsed three-manifolds with a lower curvature bound, Math. Ann. 333 (2005) 131 MR2169831
32 R Ye, Ricci flow, Einstein metrics and space forms, Trans. Amer. Math. Soc. 338 (1993) 871 MR1108615