A scalar curvature bound along the conical Kähler-Ricci flow

A note on conical Kähler-Ricci flow on minimal elliptic Kähler surfaces

“…To prove part (1) of Theorem 1.1 we first reduce the conical Kähler-Ricci flow (1.1) to a parabolic complex Monge-Ampère equation, as in, e.g., [13,17,6].…”

“…Remark 1.3. We should mention that in the setting of Theorem 1.1, it is proved in [6] that the scalar curvature of…”

The Conical Kähler–Ricci Flow with Weak Initial Data on Fano Manifolds

“…) is a smooth closed positive (1,1)form, s is the definition section of D and h is a smooth Hermitian metric on −λK M with curvature λω 0 . The smooth case of the twisted Kähler-Ricci flow was studied in [13,17,19,20,32,33,34,38,48], etc.…”

“…Later, by adopting the smooth approximation used by the authors in [34], L.M. Shen [38] [39] generalized Song-Tian's result [41] and Tian-Zhang's result [46] to the unnormalized conical Kähler-Ricci flow, and G. Edwards [17] obtained the uniform scalar curvature bound when the twisted first Chern class is negative on the foundation of Song-Tian's result [42].…”

The conical complex Monge–Ampère equations on Kähler manifolds

“…2) is the conical Kähler-Ricci flow which was studied in [10,11,15,31,32,40,41]. When β = 1, there exists no singular terms in (1.2).…”