On the lower bound of energy functionalE
1 (I)—A stability theorem on the Kähler Ricci flow |
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Authors: | Xiuxiong Chen |
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Institution: | 1. Department of Mathematics, University of Wisconsin, 53706, Madison, WI
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Abstract: | In the present article, we prove a stability theorem for the Kaehler Ricci flow near the infimum of the functional E1 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 articles. 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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Keywords: | |
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