Song–Tian's Ricci curvature bound conjecture away from singular fibers

Let $X$ be a compact Kähler manifold with semiample canonical bundle $K_X$ and intermediate Kodaira dimension $0<m<\dim X$, let $\omega_0$ be a Kähler metric on $X$, and let $\omega^\bullet(t)$ solve the Kähler–Ricci flow. Let $f:X\to B$ be the Iitaka fibration and let $S$ be the preimage of the union of the singular values of $f$ and the singular set of $B$. Song–Tian's Ricci curvature bound conjecture. The Ricci curvature of $\omega^\bullet(t)$ remains uniformly bounded on every compact subset of $X\setminus S$, independently of $t$. This is a curvature refinement of the known uniform scalar-curvature bound and is proved in the paper using the asymptotic expansion of the flow away from the singular fibers.