The $$C^{2,\alpha }$$ C 2 , α -estimate for conical Kähler–Ricci flow

Abstract

In this note, we establish a parabolic version of Tian’s $$C^{2,\alpha }$$ -estimate for conical complex Monge–Ampere equations (Tian in Chin Ann Math Ser B 38(2):687–694, 2017), which includes conical Kahler–Einstein metrics. Our estimate will complete the proof of the existence of unnormalized conical Kahler–Ricci flow in Shen (J Reine Angew Math, [28]).