Increase in topological complexity along the mean curvature flow

We construct an example of a smooth embedding of $\mathbb{S}^{p+q-1}$ in $\mathbb{R}^{p+q}$ whose evolution under the mean curvature flow forms an isolated singularity at one point, after which it is a smoothly embedded copy of $\mathbb{S}^{p-1}\times \mathbb{S}^q$. In doing so, we prove some genera