Multiplicity-one conjecture for unstable minimal-surface limits of mean curvature flow

Let $(N^n,g)$ be a Riemannian manifold and consider an almost regular mean curvature flow in $(N^n,g)$ whose long-time limit is an unstable minimal surface.

Multiplicity-one conjecture. The convergence to the unstable minimal surface must have multiplicity $1$.

This conjecture concerns whether unstable limiting minimal surfaces can arise with higher multiplicity; higher-multiplicity convergence is known to occur for stable limiting surfaces, while the unstable case remains open.