scholarly journals Convergence of Kähler–Ricci Flow on Lower-Dimensional Algebraic Manifolds of General Type

2015 ◽  
Vol 2016 (21) ◽  
pp. 6493-6511 ◽  
Author(s):  
Gang Tian ◽  
Zhenlei Zhang
Keyword(s):  
Ricci Flow ◽  
General Type ◽  
Algebraic Manifolds ◽  
Lower Dimensional

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

2006 ◽  
Vol 27 (2) ◽  
pp. 179-192 ◽  
Author(s):  
Gang Tian* ◽  
Zhou Zhang
Keyword(s):  
Ricci Flow ◽  
General Type ◽  
Projective Manifolds

scholarly journals Convergence of the Weak Kähler–Ricci Flow on Manifolds of General Type

2019 ◽  
Author(s):  
Tat Dat Tô
Keyword(s):  
Ricci Flow ◽  
General Type ◽  
Einstein Metric ◽  
Canonical Class ◽  
Open Set ◽  
Long Time Existence ◽  
Long Time ◽  
Viscosity Sense ◽  
Monge Ampere ◽  
Time Existence

Abstract We study the Kähler–Ricci flow on compact Kähler manifolds whose canonical bundle is big. We show that the normalized Kähler–Ricci flow has long-time existence in the viscosity sense, is continuous in a Zariski open set, and converges to the unique singular Kähler–Einstein metric in the canonical class. The key ingredient is a viscosity theory for degenerate complex Monge–Ampère flows in big classes that we develop, extending and refining the approach of Eyssidieux–Guedj–Zeriahi.

scholarly journals Maximal time existence of unnormalized conical Kähler–Ricci flow

2020 ◽  
Vol 2020 (760) ◽  
pp. 169-193
Author(s):  
Liangming Shen
Keyword(s):  
Ricci Flow ◽  
General Type ◽  
Normal Crossing ◽  
Log Canonical ◽  
Flow Through ◽  
Projective Manifolds ◽  
Time Existence ◽  
Simple Normal Crossing ◽  
Maximal Time ◽  
Invent Math

AbstractWe generalize the maximal time existence of Kähler–Ricci flow in [G. Tian and Z. Zhang, On the Kähler–Ricci flow on projective manifolds of general type, Chin. Ann. Math. Ser. B 27 (2006), no. 2, 179–192] and [J. Song and G. Tian, The Kähler–Ricci flow through singularities, Invent. Math. 207 (2017), no. 2, 519–595] to the conical case. Furthermore, if the log canonical bundle {K_{M}+(1-\beta)[D]} is big or big and nef, we can examine the limit behaviors of such conical Kähler–Ricci flow. Moreover, these results still hold when D is a simple normal crossing divisor.

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