Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Finite-time singularity of Kähler-Ricci flow

Pages: 1137 - 1150, Volume 28, Issue 3, November 2010      doi:10.3934/dcds.2010.28.1137

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Gang Tian - Beijing University, Beijing, 100871, China (email)

Abstract: 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:  Kähler-Ricci flow, complex Monge-Ampère equation, soliton, singularity.
Mathematics Subject Classification:  Primary: 53C44, 35J60; Secondary: 53C55.

Received: March 2010;      Revised: April 2010;      Available Online: April 2010.