Inverse mean curvature flow over non-star-shaped surfaces

We derive an upper bound on the waiting time for a variational weak solution to Inverse Mean Curvature Flow in $\mathbb{R}^{n+1}$ become star-shaped. As consequence, we demonstrate that any connected surface moving by flow which is not initially topological sphere develops singularity or self-intersection within prescribed interval depending only initial data. Finally, establish existence of either finite-time singularities intersections certain spheres under IMCF.