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July  2010, 28(3): 1137-1150. doi: 10.3934/dcds.2010.28.1137

Finite-time singularity of Kähler-Ricci flow

Gang Tian 1,

1. 

Beijing University, Beijing, 100871, China

Received  March 2010 Revised  April 2010 Published  April 2010

This is an expository paper dedicated to professor L. Nirenberg for his 85th birthday. First I will discuss my joint works with Z. Zhang and J. Song on the singularity formation of Kähler-Ricci flow. Secondly, I will show a fully nonlinear equation, scalar V-soliton equation (cf. Section 4, (14)), and some basic results about it. This equation was introduced by G. La Nave and myself in studying the singularity formation of Kähler-Ricci flow. I will also show how this new equation can be applied to studying the singularity formation at finite time.
Keywords: soliton, singularity., Kähler-Ricci flow, complex Monge-Ampère equation.
Mathematics Subject Classification: Primary: 53C44, 35J60; Secondary: 53C5.
Citation: Gang Tian. Finite-time singularity of Kähler-Ricci flow. Discrete and Continuous Dynamical Systems, 2010, 28 (3) : 1137-1150. doi: 10.3934/dcds.2010.28.1137
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