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

Volume 29
Issue 2, 549–862
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
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Collapsing Calabi–Yau fibrations and uniform diameter bounds

Yang Li

Geometry & Topology 27 (2023) 397–415
Bibliography
1 J P Demailly, N Pali, Degenerate complex Monge–Ampère equations over compact Kähler manifolds, Internat. J. Math. 21 (2010) 357 MR2647006
2 S Donaldson, S Sun, Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry, Acta Math. 213 (2014) 63 MR3261011
3 P Eyssidieux, V Guedj, A Zeriahi, A priori L–estimates for degenerate complex Monge–Ampère equations, Int. Math. Res. Not. 2008 (2008) MR2439574
4 P Eyssidieux, V Guedj, A Zeriahi, Singular Kähler–Einstein metrics, J. Amer. Math. Soc. 22 (2009) 607 MR2505296
5 M Gross, V Tosatti, Y Zhang, Collapsing of abelian fibered Calabi–Yau manifolds, Duke Math. J. 162 (2013) 517 MR3024092
6 M Gross, V Tosatti, Y Zhang, Gromov–Hausdorff collapsing of Calabi–Yau manifolds, Comm. Anal. Geom. 24 (2016) 93 MR3514555
7 B Guo, Kähler–Ricci flow on blowups along submanifolds, Math. Ann. 375 (2019) 1147 MR4023373
8 H J Hein, V Tosatti, Higher-order estimates for collapsing Calabi–Yau metrics, Camb. J. Math. 8 (2020) 683 MR4220370
9 Y Li, A gluing construction of collapsing Calabi–Yau metrics on K3 fibred 3–folds, Geom. Funct. Anal. 29 (2019) 1002 MR3990193
10 Y Li, On collapsing Calabi–Yau fibrations, J. Differential Geom. 117 (2021) 451 MR4255068
11 E D Nezza, V Guedj, H Guenancia, Families of singular Kähler–Einstein metrics, preprint (2020) arXiv:2003.08178
12 X Rong, Y Zhang, Continuity of extremal transitions and flops for Calabi–Yau manifolds, J. Differential Geom. 89 (2011) 233 MR2863918
13 J Song, Riemannian geometry of Kähler–Einstein currents, preprint (2014) arXiv:1404.0445
14 J Song, G Tian, Z Zhang, Collapsing behavior of Ricci-flat Kähler metrics and long time solutions of the Kähler–Ricci flow, preprint (2019) arXiv:1904.08345
15 S Takayama, On moderate degenerations of polarized Ricci-flat Kähler manifolds, J. Math. Sci. Univ. Tokyo 22 (2015) 469 MR3329203
16 G Tian, S T Yau, Kähler–Einstein metrics on complex surfaces with C1 > 0, Comm. Math. Phys. 112 (1987) 175 MR904143
17 V Tosatti, Adiabatic limits of Ricci-flat Kähler metrics, J. Differential Geom. 84 (2010) 427 MR2652468
18 V Tosatti, B Weinkove, X Yang, The Kähler–Ricci flow, Ricci-flat metrics and collapsing limits, Amer. J. Math. 140 (2018) 653 MR3805016
19 V Tosatti, Y Zhang, Infinite-time singularities of the Kähler–Ricci flow, Geom. Topol. 19 (2015) 2925 MR3416117