Kähler metrics with cone singularities along a divisor of bounded Ricci curvature

Let D be a smooth divisor in a compact complex manifold X and let β∈(0,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta \in (0,1)$$\end{document}. We use the liner theory developed by Donaldson (Essays in Mathematics and Its Applications, Springer, Berlin, pp 49–79, 2012) to show that in any positive co-homology class on X there is a Kähler metric with cone angle 2πβ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\pi \beta $$\end{document} along D which has bounded Ricci curvature. We use this result together with the Aubin–Yau continuity method to give an alternative proof of a well-known existence theorem for Kähler–Einstein metrics with cone singularities.