The metric Strominger–Yau–Zaslow conjecture for maximally degenerate Calabi–Yau families

Let $(X_t,g_t,J_t,\omega_t,\Omega_t)$ be a $1$-parameter maximally degenerate family of polarized $n$-dimensional Calabi–Yau manifolds of holonomy $SU(n)$ over the punctured disc $\mathbb{D}_t^*$. A special Lagrangian $T^n$-fibration is a fibration whose fibres are special Lagrangian tori with respect to the Calabi–Yau structure. Metric Strominger–Yau–Zaslow conjecture. For $0<|t|\ll 1$, there exist special Lagrangian $T^n$-fibrations on the generic region of $X_t$. This is a metric formulation of the SYZ picture for degenerating Calabi–Yau manifolds; the source later states a special Lagrangian fibration theorem on an open subset containing $W_\delta$, but the conjectural formulation concerns the generic region.