Volume 15, issue 2 (2011)

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

Volume 26
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
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
Ricci flow on open $3$–manifolds and positive scalar curvature

Laurent Bessières, Gérard Besson and Sylvain Maillot

Geometry & Topology 15 (2011) 927–975
Bibliography
1 L Bessières, G Besson, S Maillot, M Boileau, J Porti, Geometrisation of $3$–manifolds, EMS Tracts in Math. 13, Eur. Math. Soc. (2010) MR2683385
2 S Chang, S Weinberger, G Yu, Taming $3$–manifolds using scalar curvature, Geom. Dedicata 148 (2010) 3 MR2721617
3 J Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970) 61 MR0263092
4 B L Chen, S H Tang, X P Zhu, Complete classification of compact four-manifolds with positive isotropic curvature arXiv:0810.1999v1
5 B L Chen, X P Zhu, Uniqueness of the Ricci flow on complete noncompact manifolds, J. Differential Geom. 74 (2006) 119 MR2260930
6 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. Part II: Analytic aspects, Math. Surveys and Monogr. 144, Amer. Math. Soc. (2008) MR2365237
7 B Chow, P Lu, L Ni, Hamilton's Ricci flow, Graduate Studies in Math. 77, Amer. Math. Soc. (2006) MR2274812
8 J Dinkelbach, B Leeb, Equivariant Ricci flow with surgery and applications to finite group actions on geometric $3$–manifolds, Geom. Topol. 13 (2009) 1129 MR2491658
9 M Gromov, Sign and geometric meaning of curvature, Rend. Sem. Mat. Fis. Milano 61 (1991) MR1297501
10 M Gromov, H B Lawson Jr., Spin and scalar curvature in the presence of a fundamental group. I, Ann. of Math. $(2)$ 111 (1980) 209 MR569070
11 M Gromov, H B Lawson Jr., Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Études Sci. Publ. Math. (1983) 83 MR720933
12 R S Hamilton, Four-manifolds with positive isotropic curvature, Comm. Anal. Geom. 5 (1997) 1 MR1456308
13 H Huang, Complete $4$–manifolds with uniformly positive isotropic curvature arXiv:0912.5405v1
14 G Huisken, C Sinestrari, Mean curvature flow with surgeries of two-convex hypersurfaces, Invent. Math. 175 (2009) 137 MR2461428
15 B Kleiner, J Lott, Notes on Perelman's papers, Geom. Topol. 12 (2008) 2587 MR2460872
16 H Kneser, Geschlossene Flächen in dreidimensionalen Mannigfaltigkeiten, Jahresbericht D. M. V. 38 (1929) 24
17 S Maillot, A spherical decomposition for Riemannian open $3$–manifolds, Geom. Funct. Anal. 17 (2007) 839 MR2346277
18 S Maillot, Some open $3$–manifolds and $3$–orbifolds without locally finite canonical decompositions, Algebr. Geom. Topol. 8 (2008) 1795 MR2448873
19 J Morgan, G Tian, Ricci flow and the Poincaré conjecture, Clay Math. Monogr. 3, Amer. Math. Soc. (2007) MR2334563
20 G Perelman, The entropy formula for the Ricci flow and its geometric applications arXiv:math.DG/0211159
21 G Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds arXiv:math.DG/0307245
22 G Perelman, Ricci flow with surgery on three-manifolds arXiv:math.DG/0303109
23 J Rosenberg, Manifolds of positive scalar curvature: a progress report, from: "Surveys in differential geometry. Vol. XI" (editors J Cheeger, K Grove), Surv. Differ. Geom. 11, Int. Press (2007) 259 MR2408269
24 R Schoen, S T Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Ann. of Math. $(2)$ 110 (1979) 127 MR541332
25 P Scott, The geometries of $3$–manifolds, Bull. London Math. Soc. 15 (1983) 401 MR705527
26 P Scott, T Tucker, Some examples of exotic noncompact $3$–manifolds, Quart. J. Math. Oxford Ser. $(2)$ 40 (1989) 481 MR1033220
27 W X Shi, Ricci deformation of the metric on complete noncompact Riemannian manifolds, J. Differential Geom. 30 (1989) 303 MR1010165
28 M Simon, Ricci flow of almost non-negatively curved three manifolds, J. Reine Angew. Math. 630 (2009) 177 MR2526789
29 S Smale, Diffeomorphisms of the $2$–sphere, Proc. Amer. Math. Soc. 10 (1959) 621 MR0112149
30 J H C Whitehead, A certain open manifold whose group is unity, Quart. J. Math. Oxford Ser. 6 (1935) 268
31 G Xu, Short-time existence of the ricci flow on noncompact riemannian manifolds arXiv:0907.5604v1
32 S T Yau, Problem section, from: "Seminar on Differential Geometry" (editor S T Yau), Ann. of Math. Stud. 102, Princeton Univ. Press (1982) 669 MR645762