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Kähler–Ricci Flow With Small Initial Energy

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In this paper, we prove that the Kähler–Ricci flow converges to a Kähler–Einstein metric when E 1 energy is small. We also prove that E 1 is bounded from below if and only if the K-energy is bounded from below in the canonical class.

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Correspondence to Haozhao Li.

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Received: September 2006, Revision: January 2007, Accepted: February 2007

The first named author is partially supported by a NSF grant, while the third author was partially supported by a NSF supplement grant.

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Chen, X., Li, H. & Wang, B. Kähler–Ricci Flow With Small Initial Energy. GAFA Geom. funct. anal. 18, 1525–1563 (2009).

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