Do "sparkling bubbles" occur after cylindrical singularities in mean convex mean curvature flow?

Determine whether convex ancient oval solutions can appear as blow-up limits at cylindrical singularities of mean convex mean curvature flows, thereby creating tiny convex bubbles after the singular time; specifically, show that such bubbling cannot occur in the mean convex case.

Background

The authors discuss a conjectural scenario in which the blow-up at a cylindrical singularity yields compact convex ancient ovals, potentially leading to the formation of very small convex bubbles post-singularity (the “sparkling bubbles” picture).

While convex ancient flows arise as blow-up limits in mean convex settings, it remains unknown whether ovals can occur in this context; the authors conjecture that they do not, at least for mean convex flows.