Geometry & Topology Volume 24, issue 3 (2020)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

Pluripotential Kähler–Ricci flows

Vincent Guedj, Chinh H Lu and Ahmed Zeriahi

Geometry & Topology 24 (2020) 1225–1296

DOI: 10.2140/gt.2020.24.1225

Bibliography

1	E Bedford, B A Taylor, The Dirichlet problem for a complex Monge–Ampère equation, Invent. Math. 37 (1976) 1 MR445006
2	E Bedford, B A Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982) 1 MR674165
3	R J Berman, S Boucksom, P Eyssidieux, V Guedj, A Zeriahi, Kähler–Einstein metrics and the Kähler–Ricci flow on log Fano varieties, J. Reine Angew. Math. 751 (2019) 27 MR3956691
4	R J Berman, S Boucksom, V Guedj, A Zeriahi, A variational approach to complex Monge–Ampère equations, Publ. Math. Inst. Hautes Études Sci. 117 (2013) 179 MR3090260
5	H D Cao, Deformation of Kähler metrics to Kähler–Einstein metrics on compact Kähler manifolds, Invent. Math. 81 (1985) 359 MR799272
6	U Cegrell, S Kołodziej, A Zeriahi, Maximal subextensions of plurisubharmonic functions, Ann. Fac. Sci. Toulouse Math. 20 (2011) 101 MR2858169
7	T C Collins, G Székelyhidi, The twisted Kähler–Ricci flow, J. Reine Angew. Math. 716 (2016) 179 MR3518375
8	T C Collins, V Tosatti, Kähler currents and null loci, Invent. Math. 202 (2015) 1167 MR3425388
9	E Di Nezza, C H Lu, Uniqueness and short time regularity of the weak Kähler–Ricci flow, Adv. Math. 305 (2017) 953 MR3570152
10	S Dinew, An inequality for mixed Monge–Ampère measures, Math. Z. 262 (2009) 1 MR2491597
11	P Eyssidieux, V Guedj, A Zeriahi, A priori L^∞–estimates for degenerate complex Monge–Ampère equations, Int. Math. Res. Not. 2008 (2008) MR2439574
12	P Eyssidieux, V Guedj, A Zeriahi, Singular Kähler–Einstein metrics, J. Amer. Math. Soc. 22 (2009) 607 MR2505296
13	P Eyssidieux, V Guedj, A Zeriahi, Viscosity solutions to degenerate complex Monge–Ampère equations, Comm. Pure Appl. Math. 64 (2011) 1059 MR2839271
14	P Eyssidieux, V Guedj, A Zeriahi, Weak solutions to degenerate complex Monge–Ampère flows, II, Adv. Math. 293 (2016) 37 MR3474319
15	P Eyssidieux, V Guedj, A Zeriahi, Convergence of weak Kähler–Ricci flows on minimal models of positive Kodaira dimension, Comm. Math. Phys. 357 (2018) 1179 MR3769749
16	V Guedj, C H Lu, A Zeriahi, Stability of solutions to complex Monge–Ampère flows, Ann. Inst. Fourier (Grenoble) 68 (2018) 2819 MR3959096
17	V Guedj, C H Lu, A Zeriahi, Pluripotential solutions versus viscosity solutions to complex Monge–Ampère flows, preprint (2019) arXiv:1909.07069
18	V Guedj, C H Lu, A Zeriahi, Weak subsolutions to complex Monge–Ampère equations, J. Math. Soc. Japan 71 (2019) 727 MR3984240
19	V Guedj, H C Lu, A Zeriahi, The pluripotential Cauchy–Dirichlet problem for complex Monge–Ampère flows, preprint (2018) arXiv:1810.02122
20	V Guedj, A Zeriahi, Intrinsic capacities on compact Kähler manifolds, J. Geom. Anal. 15 (2005) 607 MR2203165
21	V Guedj, A Zeriahi, Stability of solutions to complex Monge–Ampère equations in big cohomology classes, Math. Res. Lett. 19 (2012) 1025 MR3039828
22	V Guedj, A Zeriahi, Degenerate complex Monge–Ampère equations, 26, Eur. Math. Soc. (2017) MR3617346
23	V Guedj, A Zeriahi, Regularizing properties of the twisted Kähler–Ricci flow, J. Reine Angew. Math. 729 (2017) 275 MR3680377
24	R S Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geometry 17 (1982) 255 MR664497
25	J Kollár, S Mori, Birational geometry of algebraic varieties, 134, Cambridge Univ. Press (1998) MR1658959
26	S Kołodziej, Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge–Ampère operator, Ann. Polon. Math. 65 (1996) 11 MR1414748
27	S Kołodziej, The complex Monge–Ampère equation, Acta Math. 180 (1998) 69 MR1618325
28	S Kołodziej, The Monge–Ampère equation on compact Kähler manifolds, Indiana Univ. Math. J. 52 (2003) 667 MR1986892
29	D H Phong, J Song, J Sturm, B Weinkove, The Kähler–Ricci flow with positive bisectional curvature, Invent. Math. 173 (2008) 651 MR2425138
30	D H Phong, J Song, J Sturm, B Weinkove, The Kähler–Ricci flow and the ∂ operator on vector fields, J. Differential Geom. 81 (2009) 631 MR2487603
31	J Song, G Székelyhidi, B Weinkove, The Kähler–Ricci flow on projective bundles, Int. Math. Res. Not. 2013 (2013) 243 MR3010688
32	J Song, G Tian, Canonical measures and Kähler–Ricci flow, J. Amer. Math. Soc. 25 (2012) 303 MR2869020
33	J Song, G Tian, The Kähler–Ricci flow through singularities, Invent. Math. 207 (2017) 519 MR3595934
34	J Song, B Weinkove, An introduction to the Kähler–Ricci flow, from: "An introduction to the Kähler–Ricci flow" (editors S Boucksom, P Eyssidieux, V Guedj), Lecture Notes in Math. 2086, Springer (2013) 89 MR3185333
35	G Tian, Z Zhang, On the Kähler–Ricci flow on projective manifolds of general type, Chinese Ann. Math. Ser. B 27 (2006) 179 MR2243679
36	T D Tô, Regularizing properties of complex Monge–Ampère flows, J. Funct. Anal. 272 (2017) 2058 MR3596716
37	V Tosatti, KAWA lecture notes on the Kähler–Ricci flow, Ann. Fac. Sci. Toulouse Math. 27 (2018) 285 MR3831026
38	V Tosatti, Y Zhang, Infinite-time singularities of the Kähler–Ricci flow, Geom. Topol. 19 (2015) 2925 MR3416117
39	H Tsuji, Existence and degeneration of Kähler–Einstein metrics on minimal algebraic varieties of general type, Math. Ann. 281 (1988) 123 MR944606
40	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