Volume 24, issue 3 (2020)

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

Volume 26
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

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 Interests
Editorial Procedure
Subscriptions
 
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
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