Kaehler-Ricci flow and the Poincare-Lelong equation

Details Kaehler-Ricci flow and the Poincare-Lelong equation Kaehler-Ricci flow and the Poincare-Lelong equation

2002-11-14

arxiv.org/abs/math/0211219v1

Mathematics

Differential Geometry

to appear in Communications in Analysis and Geometry

Scientific paper

We show that the solution constructed in an earlier work of Y-G. Shi and the authors can be used to obtain sharp gradient estimates for the Kaehler-Ricci flow which achieves equality on a steady soliton. The estimate can be applied to obtain a long time existence of the Kaehler-Ricci flow. In the second part of the paper we develope a so-called "moment" type estimate for the Kaehler-Ricci flow, through which we prove that the flow preserves several properties. In the last part we study the convergence of the Kaehler-Ricci flow.

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