Let $\Sigma$ be a wildly embedded 2-sphere in 3-sphere $S^3$. For simplicity, we may assume that $\Sigma$ is the Alexander horned sphere.
Question. Can we define the mean curvature flow (MCF) starting with $\Sigma$ and evolving towards a smoothly embedded 2-sphere (within a short time)? If not, are there other curvature flows can capture such a phenomenon?
