Geometry & Topology Volume 19, issue 5 (2015)

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Infinite-time singularities of the Kähler–Ricci flow

Valentino Tosatti and Yuguang Zhang

Geometry & Topology 19 (2015) 2925–2948

DOI: 10.2140/gt.2015.19.2925

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)