On the Kähler-Ricci Flow on Projective Manifolds of General Type

Gang Tian* , Zhou Zhang

Chinese Annals of Mathematics, Series B ›› 2006, Vol. 27 ›› Issue (2) : 179 -192.

PDF
Chinese Annals of Mathematics, Series B ›› 2006, Vol. 27 ›› Issue (2) : 179 -192. DOI: 10.1007/s11401-005-0533-x
Original Articles

On the Kähler-Ricci Flow on Projective Manifolds of General Type

Author information +
History +
PDF

Abstract

This note concerns the global existence and convergence of the solution for Kähler-Ricci flow equation when the canonical class, K X, is numerically effective and big. We clarify some known results regarding this flow on projective manifolds of general type and also show some new observations and refined results.

Keywords

Geometric evolution equations / Minimal model program / 53C44 / 14E30

Cite this article

Download citation ▾
Gang Tian*, Zhou Zhang. On the Kähler-Ricci Flow on Projective Manifolds of General Type. Chinese Annals of Mathematics, Series B, 2006, 27(2): 179-192 DOI:10.1007/s11401-005-0533-x

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Bedford Acta Math., 1982, 149: 1

[2]

Cao Invent. Math., 1985, 81: 359

[3]

Cascini, P. and La Nave, G., Kähler-Ricci flow and the minimal model program for projective varieties, preprint.

[4]

Demailly, J.-P., Complex analytic and algebraic geometry, Online book: agbook.ps.gz.

[5]

Durfee Enseign. Math., 1979, 25: 131

[6]

Feldman J. Diff. Geom., 2003, 65: 169

[7]

Gilbarg, D. and Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, 2nd edition, Grundlehren der Mathematischen Wissenschaften, 224.

[8]

Kawamata Ann. of Math., 1984, 119: 603

[9]

Kawamata Invent. Math., 1985, 79: 567

[10]

Kawamata Math. Ann., 1982, 261: 43

[11]

Kleiman Ann. of Math., 1966, 84: 293

[12]

Kobayashi Math. Ann., 1985, 272: 385

[13]

Kolodziej Acta Math., 1998, 180: 69

[14]

Nakamaye Math. Ann., 2000, 318: 837

[15]

Sugiyama, K., Einstein-Kähler metrics on minimal varieties of general type and an inequality between Chern numbers, Recent Topics in Differential and Analytic Geometry, 417-433; Adv. Stud. Pure Math., 18-1, Academic Press, Boston, MA, 1990.

[16]

Tian, G., Geometry and nonlinear analysis, Proceedings of the International Congress of Mathematicians (Beijing 2002), Vol. I, Higher Ed. Press, Beijing, 2002, 475-493.

[17]

Tsuji Math. Ann., 1988, 281: 123

[18]

Tsuji, H., Degenerated Monge-Ampere equation in algebraic geometry, Miniconference on Analysis and Applications (Brisbane, 1993), Proc. Centre Math. Appl. Austral. Nat. Univ., 33, Austral. Nat. Univ., Canberra, 1994, 209-224.

[19]

Yau Comm. Pure Appl. Math., 1978, 31: 339

[20]

Zariski Ann. of Math., 1962, 76: 560

[21]

Zhang, Z., Thesis in preparation.

AI Summary AI Mindmap
PDF

127

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/