Communications in Analysis and Geometry

Volume 19 (2011)

Number 5

On convergence of the Kähler–Ricci flow

Pages: 887 – 903



Ovidiu Munteanu (Department of Mathematics, Columbia University)

Gábor Székelyhidi (Department of Mathematics, University of Notre Dame, Notre Dame, Indiana)


We study the convergence of the Kähler–Ricci flow on aFano manifold under some stability conditions. Moreprecisely we assume that the first eingenvalue of the$\bar{\partial}$-operator acting on vector fields isuniformly bounded along the flow, and in addition theMabuchi energy decays at most logarithmically. We then givedifferent situations in which the condition on the Mabuchienergy holds.

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