On the Kahler-Ricci flow with small initial E_1 energy (I)
  In this paper, we prove that the Kahler Ricci flow converges to a Kahler 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. 
Xiuxiong Chen, Haozhao Li and Bing Wang