Uniform curvature bound conjecture for inverse mean curvature flow in Euclidean three-space

Let $\{N_t\}_{0 \leq t < T_{\max}}$ be a solution to inverse mean curvature flow in $\mathbb{R}^3$, with second fundamental form $A$.

Uniform curvature bound conjecture. The curvature remains uniformly bounded up to the maximal time:

$$\max_{N \times [0,T_{\max})} |A|(x,t) < +\infty.$$

The conjecture would rule out curvature blow-up and the proposed noncompact minimal blow-up limits for singular inverse mean curvature flow solutions. The supplied material gives no resolution, so its status remains open.