Greene–Wu conjecture on uniform equivalence of the Kobayashi metric

Let $(M,h)$ be a simply-connected complete Kähler manifold satisfying

$$-A \leq \operatorname{sectional\ curvature} \leq -B$$

for two positive constants $A$ and $B$. Let $\mathfrak{K}$ denote the Kobayashi metric on $M$. Greene–Wu's conjecture. There is a constant $C>0$, depending only on $A$ and $B$, such that

$$C^{-1}h(z;v) \leq \mathfrak{K}^2(z;v) \leq Ch(z;v), \qquad \forall z\in M,\ \forall v\in T_z^{1,0}M.$$

This conjecture asks for uniform equivalence between the Kobayashi–Royden metric and the Kähler metric under two-sided negative sectional-curvature bounds. The supplied text gives no resolution, so the conjecture is recorded as open.