Logarithmic Tian–Yau–Donaldson conjecture for conic Kähler metrics

Let $(X,Y)$ be a pair consisting of a compact Kähler manifold $X$ and a divisor $Y$, and let $(X,Y)$ be log-K-stable in the logarithmic sense. A constant scalar curvature conic Kähler metric on $(X,Y)$ is a Kähler metric with conical singularities along $Y$. Logarithmic Tian–Yau–Donaldson conjecture. There is a constant scalar curvature conic Kähler metric on $(X,Y)$ if and only if $(X,Y)$ is log-K-stable. This is the logarithmic analogue of the Tian–Yau–Donaldson conjecture, motivated in the source by the explicitly solved case of conic metrics on $\mathbb{P}^1$; the general statement is presented as a conjectural extension.