Yau's ampleness conjecture for manifolds with negative holomorphic sectional curvature

Let $(X,\omega)$ be a compact Kähler manifold with strictly negative holomorphic sectional curvature, and let $K_X$ denote its canonical line bundle. Yau's ampleness conjecture. The canonical line bundle $K_X$ is ample. This conjecture relates differential-geometric negativity of holomorphic sectional curvature to algebraic positivity of the canonical bundle; its resolution is not established by the supplied text.