Volume 19, issue 5 (2015)

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

Volume 29
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

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
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
Infinite-time singularities of the Kähler–Ricci flow

Valentino Tosatti and Yuguang Zhang

Geometry & Topology 19 (2015) 2925–2948
Bibliography
1 R H Bamler, Long-time analysis of 3–dimensional Ricci flow, III, arXiv:1310.4483
2 W P Barth, K Hulek, C A M Peters, A Van de Ven, Compact complex surfaces, 4, Springer (2004) MR2030225
3 H D Cao, Deformation of Kähler metrics to Kähler–Einstein metrics on compact Kähler manifolds, Invent. Math. 81 (1985) 359 MR799272
4 F Catanese, Deformation in the large of some complex manifolds, I, Ann. Mat. Pura Appl. 183 (2004) 261 MR2082659
5 F T H Fong, Z Zhang, The collapsing rate of the Kähler–Ricci flow with regular infinite time singularity, J. Reine Angew. Math. 703 (2015) 95 MR3353543
6 R Friedman, J W Morgan, Smooth four-manifolds and complex surfaces, 27, Springer (1994) MR1288304
7 M Gill, Collapsing of products along the Kähler–Ricci flow, Trans. Amer. Math. Soc. 366 (2014) 3907 MR3192623
8 M Gross, V Tosatti, Y Zhang, Collapsing of abelian fibered Calabi–Yau manifolds, Duke Math. J. 162 (2013) 517 MR3024092
9 M Gross, V Tosatti, Y Zhang, Gromov–Hausdorff collapsing of Calabi–Yau manifolds, arXiv:1304.1820
10 R S Hamilton, The Ricci flow on surfaces, from: "Mathematics and general relativity" (editor J A Isenberg), Contemp. Math. 71, Amer. Math. Soc. (1988) 237 MR954419
11 H J Hein, V Tosatti, Remarks on the collapsing of torus fibered Calabi–Yau manifolds, arXiv:1402.0610
12 Y Kawamata, On the length of an extremal rational curve, Invent. Math. 105 (1991) 609 MR1117153
13 Y Kawamata, Flops connect minimal models, Publ. Res. Inst. Math. Sci. 44 (2008) 419 MR2426353
14 K Kodaira, Complex manifolds and deformation of complex structures, Springer, Berlin (2005) MR2109686
15 J Lott, On the long-time behavior of type-III Ricci flow solutions, Math. Ann. 339 (2007) 627 MR2336062
16 D McDuff, D Salamon, J–holomorphic curves and symplectic topology, 52, Amer. Math. Soc. (2004) MR2045629
17 D H Phong, J Sturm, On stability and the convergence of the Kähler–Ricci flow, J. Differential Geom. 72 (2006) 149 MR2215459
18 D Riebesehl, F Schulz, A priori estimates and a Liouville theorem for complex Monge–Ampère equations, Math. Z. 186 (1984) 57 MR735051
19 M Sherman, B Weinkove, Interior derivative estimates for the Kähler–Ricci flow, Pacific J. Math. 257 (2012) 491 MR2972475
20 J Song, G Tian, Bounding scalar curvature for global solutions of the Kähler–Ricci flow, arXiv:1111.5681
21 J Song, G Tian, The Kähler–Ricci flow on surfaces of positive Kodaira dimension, Invent. Math. 170 (2007) 609 MR2357504
22 J Song, G Tian, Canonical measures and Kähler–Ricci flow, J. Amer. Math. Soc. 25 (2012) 303 MR2869020
23 G Tian, Z Zhang, On the Kähler–Ricci flow on projective manifolds of general type, Chinese Ann. Math. Ser. B 27 (2006) 179 MR2243679
24 V Tosatti, Adiabatic limits of Ricci-flat Kähler metrics, J. Differential Geom. 84 (2010) 427 MR2652468
25 V Tosatti, Degenerations of Calabi–Yau metrics, Acta Phys. Polon. B Proc. Suppl. 4 (2011) 495
26 V Tosatti, Calabi–Yau manifolds and their degenerations, Ann. N. Y. Acad. Sci. 1260 (2012) 8
27 V Tosatti, B Weinkove, X Yang, The Kähler–Ricci flow, Ricci-flat metrics and collapsing limits, arXiv:1408.0161
28 Y Wang, A Liouville theorem for the complex Monge–Ampère equation, arXiv:1303.2403
29 S T Yau, A general Schwarz lemma for Kähler manifolds, Amer. J. Math. 100 (1978) 197 MR0486659
30 S T Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge–Ampère equation, I, Comm. Pure Appl. Math. 31 (1978) 339 MR480350
31 Y Zhang, Convergence of Kähler manifolds and calibrated fibrations, PhD thesis, Nankai Institute of Mathematics (2006)