The global structure of bi-rotational self-expanders

We describe the self-expanders of the mean curvature flow in $\mathbb{R}^{p+q+2}$ invariant under $O(p+1)\times O(q+1)$. Apart from the Clifford minimal cone, every such hypersurface is complete, proper and noncompact, and belongs to one of three families: two one-parameter families of embedded hype