A note on Kähler–Ricci flow

Let g(t) with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${t\in [0,T)}$$\end{document} be a complete solution to the Kähler–Ricci flow: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\frac{d}{dt}g_{i\bar j}=-R_{i\bar j}}$$\end{document} where T may be ∞. In this article, we show that the curvature of g(t) is uniformly bounded if the solution g(t) is uniformly equivalent. This result is stronger than the main result in Šešum (Am J Math 127(6):1315–1324, 2005) within the category of Kähler–Ricci flow.