Yau's Kähler–Einstein stability conjecture for Fano manifolds

Let $V$ be a Fano manifold, and let stable mean stable in the sense of Geometric Invariant Theory. Yau's conjecture. The manifold $V$ admits a Kähler–Einstein metric if and only if it is stable in the sense of Geometric Invariant Theory.

The conjecture links the existence of Kähler–Einstein metrics on Fano manifolds with algebraic stability and is presented as a major open conjecture in Kähler geometry. No resolution is supplied in the paper.