Bounded curvature conjecture for the Hodge metric on Calabi–Yau threefold moduli

Let $\mathcal M$ be the moduli space of a Calabi–Yau threefold, and let $\omega_H$ denote its Hodge metric.

Bounded-curvature conjecture. The curvature of the Hodge metric $\omega_H$ is bounded.

This conjecture concerns the behavior of the Hodge metric near infinity in Calabi–Yau moduli space. The supplied source does not state whether the conjecture has been proved or disproved.