Smooth approximations of the conical Kähler–Ricci flows

In this note, we show that the conical Kähler–Ricci flows introduced in Chen and Wang (Bessel functions, Heat kernel and the conical Kähler–Ricci flow. J. Funct. Anal. 269(2), 2013) exist for all time t∈[0,∞)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t\in [0,\infty )$$\end{document} in the weak sense as in Definition 1.2. As a key ingredient of the proof, we show that a conical Kähler–Ricci flow is actually the limit of a sequence of smooth Kähler–Ricci flows.