On the lower bound of energy functional E_1 (I)-- a stability theorem on the Kaehler Ricci flow

Details On the lower bound of energy functional E_1 (I)-- a stability theorem on the Kaehler Ricci flow On the lower bound of energy functional E_1 (I)-- a stability theorem on the Kaehler Ricci flow

2005-02-09

arxiv.org/abs/math/0502196v1

Mathematics

Differential Geometry

23 pages

Scientific paper

In the present paper, we prove a stability theorem for the Kaehler Ricci flow near the infimum of the functional E_1 under the assumption that the initial metric has Ricci > -1 and |Riem| bounded. At present stage, our main theorem still need a topological assumption (1.2) which we hope to be removed in subsequent papers. The underlying moral is: if a Kaehler metric is sufficiently closed to a Kaehler Einstein metric, then the Kaehler Ricci flow converges to it. The present work should be viewed as a first step in a more ambitious program of deriving the existence of Kaehler Einstein metrics with an arbitrary energy level, provided that this energy functional has a uniform lower bound in this Kaehler class.

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