Unnormalize conical K\"ahler-Ricci flow

Abstract

We generalize the maximal time existence of K\"{a}hler-Ricci flow in Tian-Zhang and Song-Tian to conical case. Furthermore, if the twisted canonical bundle $K_{M}+(1-\beta)[D]$ is big or big and nef, we can expect more on the limit behaviors of such conical K\"{a}hler-Ricci flow. Moreover, the results still hold for simple normal crossing divisor.