Regularity of the level set flow
Tobias Holck Colding, William P. Minicozzi II,
2016.06.16
http://arxiv.org/abs/1606.05185
We showed earlier that the level set function of a monotonic advancing front
is twice differentiable everywhere with bounded second derivative. We show here
that the second derivative is continuous if and only if the flow has a single
singular time where it becomes extinct and the singular set consists of a
closed $C^1$ manifold with cylindrical singularities.
