CR Yau uniformization conjecture for Sasakian manifolds

Let $M$ be a complete noncompact Sasakian $(2n+1)$-manifold with positive pseudohermitian bisectional curvature. Let $\mathbf{H}_n=\mathbb{C}^n\times\mathbb{R}$ be the standard $(2n+1)$-dimensional Heisenberg group. CR Yau uniformization conjecture. The manifold $M$ is CR biholomorphic to $\mathbf{H}_n$. This is presented as the third CR Yau uniformization conjecture and is the CR analogue of Yau's positive-curvature uniformization problem; no resolution is given in the supplied text.