On the cone conjecture for certain pairs of dimension at most 4

In this paper, by running MMP and considering the anti-canonical fibration, we prove the Morrison-Kawamata cone conjecture for klt Calabi-Yau pairs $(X,\mathrm{\Delta })$ such that $\dim X$ is at most $4$, and the Iitaka dimension $\kappa (X,-K_X)$ is at least $\dim X-2$.