Mathematical Research Letters

Volume 21 (2014)

Number 6

Finite-time extinction of the Kähler–Ricci flow

Pages: 1435 – 1449



Jian Song (Department of Mathematics, Rutgers University, Piscataway, New Jersey, U.S.A.)


We investigate the limiting behavior of the unnormalized Kähler–Ricci flow on a Kähler manifold with a polarized initial Kähler metric.We prove that the Kähler–Ricci flow becomes extinct in finite time if and only if the manifold has positive first Chern class and the initial Kähler class is proportional to the first Chern class of the manifold. This proves a conjecture of Tian for the smooth solutions of the Kähler–Ricci flow.

Published 2 April 2015