Geometry & Topology Volume 22, issue 6 (2018)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Kähler–Ricci flow, Kähler–Einstein metric, and K–stability

Xiuxiong Chen, Song Sun and Bing Wang

Geometry & Topology 22 (2018) 3145–3173

DOI: 10.2140/gt.2018.22.3145

Bibliography

1	R J Berman, D Witt Nyström, Complex optimal transport and the pluripotential theory of Kähler–Ricci solitons, preprint (2014) arXiv:1401.8264
2	E Calabi, X X Chen, The space of Kähler metrics, II, J. Differential Geom. 61 (2002) 173 MR1969662
3	X Chen, S Donaldson, S Sun, Kähler–Einstein metrics on Fano manifolds, I : Approximation of metrics with cone singularities, J. Amer. Math. Soc. 28 (2015) 183 MR3264766
4	X Chen, S Donaldson, S Sun, Kähler–Einstein metrics on Fano manifolds, II : Limits with cone angle less than 2π, J. Amer. Math. Soc. 28 (2015) 199 MR3264767
5	X Chen, S Donaldson, S Sun, Kähler–Einstein metrics on Fano manifolds, III : Limits as cone angle approaches 2π and completion of the main proof, J. Amer. Math. Soc. 28 (2015) 235 MR3264768
6	X X Chen, W Y He, On the Calabi flow, Amer. J. Math. 130 (2008) 539 MR2405167
7	X Chen, W He, The Calabi flow on Kähler surfaces with bounded Sobolev constant, I, Math. Ann. 354 (2012) 227 MR2957626
8	X Chen, S Sun, Calabi flow, geodesic rays, and uniqueness of constant scalar curvature Kähler metrics, Ann. of Math. 180 (2014) 407 MR3224716
9	X Chen, B Wang, Space of Ricci flows, I, Comm. Pure Appl. Math. 65 (2012) 1399 MR2957704
10	X Chen, B Wang, The Kähler Ricci flow on Fano manifolds, I, J. Eur. Math. Soc. 14 (2012) 2001 MR2984594
11	X Chen, B Wang, Space of Ricci flows, II, A : Moduli of singular Calabi–Yau spaces, Forum Math. Sigma 5 (2017) MR3739253
12	X X Chen, B Wang, Space of Ricci flows, II, B: Weak compactness of the flow,
13	T Darvas, The Mabuchi completion of the space of Kähler potentials, Amer. J. Math. 139 (2017) 1275 MR3702499
14	T Darvas, W He, Geodesic rays and Kähler–Ricci trajectories on Fano manifolds, Trans. Amer. Math. Soc. 369 (2017) 5069 MR3632560
15	V Datar, G Székelyhidi, Kähler–Einstein metrics along the smooth continuity method, Geom. Funct. Anal. 26 (2016) 975 MR3558304
16	S K Donaldson, Scalar curvature and stability of toric varieties, J. Differential Geom. 62 (2002) 289 MR1988506
17	S K Donaldson, Lower bounds on the Calabi functional, J. Differential Geom. 70 (2005) 453 MR2192937
18	S K Donaldson, Kähler metrics with cone singularities along a divisor, from: "Essays in mathematics and its applications" (editors P M Pardalos, T M Rassias), Springer (2012) 49 MR2975584
19	S K Donaldson, Stability, birational transformations and the Kahler–Einstein problem, from: "Surveys in differential geometry" (editors H D Cao, S T Yau), Surv. Differ. Geom. 17, International (2012) 203 MR3076062
20	S Donaldson, S Sun, Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry, Acta Math. 213 (2014) 63 MR3261011
21	S Donaldson, S Sun, Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry, II, J. Differential Geom. 107 (2017) 327 MR3707646
22	R Feng, H Huang, The global existence and convergence of the Calabi flow on ℂⁿ∕ℤⁿ + iℤⁿ, J. Funct. Anal. 263 (2012) 1129 MR2927407
23	A Futaki, T Mabuchi, Bilinear forms and extremal Kähler vector fields associated with Kähler classes, Math. Ann. 301 (1995) 199 MR1314584
24	V Georgoulas, J W Robbin, D A Salamon, The moment-weight inequality and the Hilbert–Mumford criterion, preprint (2013) arXiv:1311.0410
25	U Görtz, T Wedhorn, Algebraic geometry, I : Schemes with examples and exercises, Vieweg + Teubner (2010) MR2675155
26	W He, On the convergence of the Calabi flow, Proc. Amer. Math. Soc. 143 (2015) 1273 MR3293741
27	H Li, B Wang, K Zheng, Regularity scales and convergence of the Calabi flow, To appear in J. Geom. Anal. (2017)
28	S T Paul, Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics, Ann. of Math. 175 (2012) 255 MR2874643
29	S T Paul, A numerical criterion for K–energy maps of algebraic manifolds, preprint (2012) arXiv:1210.0924
30	S T Paul, Stable pairs and coercive estimates for the Mabuchi functional, preprint (2013) arXiv:1308.4377
31	D H Phong, N Sesum, J Sturm, Multiplier ideal sheaves and the Kähler–Ricci flow, Comm. Anal. Geom. 15 (2007) 613 MR2379807
32	N Sesum, G Tian, Bounding scalar curvature and diameter along the Kähler Ricci flow (after Perelman), J. Inst. Math. Jussieu 7 (2008) 575 MR2427424
33	J Streets, Long time existence of minimizing movement solutions of Calabi flow, Adv. Math. 259 (2014) 688 MR3197669
34	S Sun, Y Wang, On the Kähler–Ricci flow near a Kähler–Einstein metric, J. Reine Angew. Math. 699 (2015) 143 MR3305923
35	G Székelyhidi, Extremal metrics and K–stability, Bull. Lond. Math. Soc. 39 (2007) 76 MR2303522
36	G Székelyhidi, The Kähler–Ricci flow and K–polystability, Amer. J. Math. 132 (2010) 1077 MR2663648
37	G Székelyhidi, Filtrations and test-configurations, Math. Ann. 362 (2015) 451 MR3343885
38	G Székelyhidi, The partial C⁰–estimate along the continuity method, J. Amer. Math. Soc. 29 (2016) 537 MR3454382
39	G Tian, Kähler–Einstein metrics with positive scalar curvature, Invent. Math. 130 (1997) 1 MR1471884
40	G Tian, Z Zhang, Regularity of Kähler–Ricci flows on Fano manifolds, Acta Math. 216 (2016) 127 MR3508220
41	G Tian, X Zhu, A new holomorphic invariant and uniqueness of Kähler–Ricci solitons, Comment. Math. Helv. 77 (2002) 297 MR1915043
42	V Tosatti, Kähler–Ricci flow on stable Fano manifolds, J. Reine Angew. Math. 640 (2010) 67 MR2629688
43	V Tosatti, B Weinkove, The Calabi flow with small initial energy, Math. Res. Lett. 14 (2007) 1033 MR2357473
44	D Witt Nyström, Test configurations and Okounkov bodies, Compos. Math. 148 (2012) 1736 MR2999302
45	S T Yau, Open problems in geometry, from: "Differential geometry: partial differential equations on manifolds" (editor R Greene), Proc. Sympos. Pure Math. 54, Amer. Math. Soc. (1993) 1 MR1216573