Yang–Zheng's conjecture on real bisectional curvature

Let $M$ be a Hermitian manifold with a Hermitian metric $g$. Assume that $g$ has positive or quasi-positive real bisectional curvature. Yang–Zheng's conjecture. Then $M$ is projective and rationally connected. This is presented as a Hermitian generalization of Yau's conjecture; the supplied status evidence resolves the rational-connectedness conclusion, so the conjecture is recorded as solved.