Yang's conjecture on quasi-positive holomorphic sectional curvature and rational connectedness

Let $X$ be a compact Kähler manifold, and let $TX$ denote its holomorphic tangent bundle. A Hermitian metric $c9$ on $TX$ is assumed to be uniformly RC-quasi-positive, or equivalently in the stated alternative to have quasi-positive holomorphic sectional curvature. Yang's conjecture. If $TX$ admits such a Hermitian metric, then $X$ is projective and rationally connected. This conjecture concerns a proposed differential-geometric criterion for projectivity and rational connectedness. The source proves a quasi-positive curvature-to-positivity result for vector bundles, but does not state that Yang's conjecture is resolved.