Instantaneously complete Chern–Ricci flow and Kähler–Einstein metrics

In this work, we obtain some existence results of Chern–Ricci Flows and the corresponding Potential Flows on complex manifolds with possibly incomplete initial data. We discuss the behaviour of the solution as t→ 0. These results can be viewed as a generalization of an existence result of Ricci flow by Giesen and Topping for surfaces of hyperbolic type to higher dimensions in certain sense. On the other hand, we also discuss the long time behaviour of the solution and obtain some sufficient conditions for the existence of Kähler-Einstein metric on complete non-compact Hermitian manifolds, which generalizes the work of Lott–Zhang and Tosatti–Weinkove to complete non-compact Hermitian manifolds with possibly unbounded curvature.