Generalized Kähler–Ricci-flow convergence conjecture

Let $(M^{2n},g,b,I,J)$ be a compact generalized Kähler manifold with holomorphically trivial canonical bundles. The generalized Kähler–Ricci flow is the flow starting from this initial generalized Kähler structure, and its generalized Kähler class is the corresponding class of the initial data.

Generalized Kähler–Ricci-flow convergence conjecture. The generalized Kähler–Ricci flow preserves the generalized Kähler class, exists for all time, and converges to the unique generalized Calabi–Yau geometry $(g_{\infty},b_{\infty},I,J_{\infty})$ in this class, where $(g_{\infty},I)$ and $(g_{\infty},J_{\infty})$ are both Kähler Ricci-flat.

This is a refinement of the generalized Kähler Calabi–Yau conjecture and is motivated by the formal properties and monotonicity estimates of the flow. The paper proves global existence and convergence under the additional assumption that the relevant class contains a fixed point of the flow; removing that assumption remains open.