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We show that on a smooth Hermitian minimal model of general type theChern-Ricci flow converges to a closed positive current on M. Moreover, theflow converges smoothly to a Kahler-Einstein metric on compact sets away fromthe null locus of K_M. This generalizes work of Tsuji and Tian-Zhang toHermitian manifolds, providing further evidence that the Chern-Ricci flow is anatural generalization of the Kahler-Ricci flow.

The Chern-Ricci flow on smooth minimal models of general type