Kähler-Ricci flow with degenerate initial class

Zhang, Zhou

doi:10.1090/S0002-9947-2014-05943-6

Kähler-Ricci flow with degenerate initial class
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Trans. Amer. Math. Soc. 366 (2014), 3389-3403 Request permission

Abstract:

In an earlier joint work with X. X. Chen and G. Tian (2011), we introduced the weak Kähler-Ricci flow for various geometric motivations. In this current work, we give further consideration to setting up the weak flow by allowing the initial class to be not necessarily Kähler. It’s shown that the construction is compatible with the earlier construction in the Kähler case. We also discuss the convergence as $t\to 0^+$, which is of great interest in this topic, and provide related motivation.

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